a from scale-rotated-ellipse

Average Error: 63.5 → 40.6

Time: 2.1min

Precision: binary64

Cost: 39748

Math

\[\frac{-\sqrt{\left(\left(2 \cdot \frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}\right) \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)\right) \cdot \left(\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} + \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right) + \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}\right)}}{\frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}} \]

↓

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\mathsf{hypot}\left(b \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right), a \cdot \cos t_0\right) \cdot \left(\left(x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\left(x-scale \cdot \left(\sqrt{8} \cdot \mathsf{hypot}\left(a, b \cdot \sin t_0\right)\right)\right) \cdot 0.25\right)\\ \end{array} \]

FPCore

(FPCore (a b angle x-scale y-scale)
 :precision binary64
 (/
  (-
   (sqrt
    (*
     (*
      (* 2.0 (/ (* 4.0 (* (* b a) (* b (- a)))) (pow (* x-scale y-scale) 2.0)))
      (* (* b a) (* b (- a))))
     (+
      (+
       (/
        (/
         (+
          (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
          (pow (* b (cos (* (/ angle 180.0) PI))) 2.0))
         x-scale)
        x-scale)
       (/
        (/
         (+
          (pow (* a (cos (* (/ angle 180.0) PI))) 2.0)
          (pow (* b (sin (* (/ angle 180.0) PI))) 2.0))
         y-scale)
        y-scale))
      (sqrt
       (+
        (pow
         (-
          (/
           (/
            (+
             (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
             (pow (* b (cos (* (/ angle 180.0) PI))) 2.0))
            x-scale)
           x-scale)
          (/
           (/
            (+
             (pow (* a (cos (* (/ angle 180.0) PI))) 2.0)
             (pow (* b (sin (* (/ angle 180.0) PI))) 2.0))
            y-scale)
           y-scale))
         2.0)
        (pow
         (/
          (/
           (*
            (*
             (* 2.0 (- (pow b 2.0) (pow a 2.0)))
             (sin (* (/ angle 180.0) PI)))
            (cos (* (/ angle 180.0) PI)))
           x-scale)
          y-scale)
         2.0)))))))
  (/ (* 4.0 (* (* b a) (* b (- a)))) (pow (* x-scale y-scale) 2.0))))

↓

(FPCore (a b angle x-scale y-scale)
 :precision binary64
 (let* ((t_0 (* angle (* PI 0.005555555555555556))))
   (if (<= x-scale -4.0824742066359556e-166)
     (*
      (hypot (* b (sin (* PI (* 0.005555555555555556 angle)))) (* a (cos t_0)))
      (* (* x-scale (pow 16.0 0.5)) -0.25))
     (if (<= x-scale 1.9291306953128207e-163)
       (* b y-scale)
       (*
        (sqrt 2.0)
        (* (* x-scale (* (sqrt 8.0) (hypot a (* b (sin t_0))))) 0.25))))))

C

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return -sqrt((((2.0 * ((4.0 * ((b * a) * (b * -a))) / pow((x_45_scale * y_45_scale), 2.0))) * ((b * a) * (b * -a))) * (((((pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(((angle / 180.0) * ((double) M_PI)))), 2.0)) / x_45_scale) / x_45_scale) + (((pow((a * cos(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * sin(((angle / 180.0) * ((double) M_PI)))), 2.0)) / y_45_scale) / y_45_scale)) + sqrt((pow(((((pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(((angle / 180.0) * ((double) M_PI)))), 2.0)) / x_45_scale) / x_45_scale) - (((pow((a * cos(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * sin(((angle / 180.0) * ((double) M_PI)))), 2.0)) / y_45_scale) / y_45_scale)), 2.0) + pow((((((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((angle / 180.0) * ((double) M_PI)))) * cos(((angle / 180.0) * ((double) M_PI)))) / x_45_scale) / y_45_scale), 2.0)))))) / ((4.0 * ((b * a) * (b * -a))) / pow((x_45_scale * y_45_scale), 2.0));
}

↓

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = angle * (((double) M_PI) * 0.005555555555555556);
	double tmp;
	if (x_45_scale <= -4.0824742066359556e-166) {
		tmp = hypot((b * sin((((double) M_PI) * (0.005555555555555556 * angle)))), (a * cos(t_0))) * ((x_45_scale * pow(16.0, 0.5)) * -0.25);
	} else if (x_45_scale <= 1.9291306953128207e-163) {
		tmp = b * y_45_scale;
	} else {
		tmp = sqrt(2.0) * ((x_45_scale * (sqrt(8.0) * hypot(a, (b * sin(t_0))))) * 0.25);
	}
	return tmp;
}

Java

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return -Math.sqrt((((2.0 * ((4.0 * ((b * a) * (b * -a))) / Math.pow((x_45_scale * y_45_scale), 2.0))) * ((b * a) * (b * -a))) * (((((Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((angle / 180.0) * Math.PI))), 2.0)) / x_45_scale) / x_45_scale) + (((Math.pow((a * Math.cos(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.sin(((angle / 180.0) * Math.PI))), 2.0)) / y_45_scale) / y_45_scale)) + Math.sqrt((Math.pow(((((Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((angle / 180.0) * Math.PI))), 2.0)) / x_45_scale) / x_45_scale) - (((Math.pow((a * Math.cos(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.sin(((angle / 180.0) * Math.PI))), 2.0)) / y_45_scale) / y_45_scale)), 2.0) + Math.pow((((((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin(((angle / 180.0) * Math.PI))) * Math.cos(((angle / 180.0) * Math.PI))) / x_45_scale) / y_45_scale), 2.0)))))) / ((4.0 * ((b * a) * (b * -a))) / Math.pow((x_45_scale * y_45_scale), 2.0));
}

↓

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = angle * (Math.PI * 0.005555555555555556);
	double tmp;
	if (x_45_scale <= -4.0824742066359556e-166) {
		tmp = Math.hypot((b * Math.sin((Math.PI * (0.005555555555555556 * angle)))), (a * Math.cos(t_0))) * ((x_45_scale * Math.pow(16.0, 0.5)) * -0.25);
	} else if (x_45_scale <= 1.9291306953128207e-163) {
		tmp = b * y_45_scale;
	} else {
		tmp = Math.sqrt(2.0) * ((x_45_scale * (Math.sqrt(8.0) * Math.hypot(a, (b * Math.sin(t_0))))) * 0.25);
	}
	return tmp;
}

Python

def code(a, b, angle, x_45_scale, y_45_scale):
	return -math.sqrt((((2.0 * ((4.0 * ((b * a) * (b * -a))) / math.pow((x_45_scale * y_45_scale), 2.0))) * ((b * a) * (b * -a))) * (((((math.pow((a * math.sin(((angle / 180.0) * math.pi))), 2.0) + math.pow((b * math.cos(((angle / 180.0) * math.pi))), 2.0)) / x_45_scale) / x_45_scale) + (((math.pow((a * math.cos(((angle / 180.0) * math.pi))), 2.0) + math.pow((b * math.sin(((angle / 180.0) * math.pi))), 2.0)) / y_45_scale) / y_45_scale)) + math.sqrt((math.pow(((((math.pow((a * math.sin(((angle / 180.0) * math.pi))), 2.0) + math.pow((b * math.cos(((angle / 180.0) * math.pi))), 2.0)) / x_45_scale) / x_45_scale) - (((math.pow((a * math.cos(((angle / 180.0) * math.pi))), 2.0) + math.pow((b * math.sin(((angle / 180.0) * math.pi))), 2.0)) / y_45_scale) / y_45_scale)), 2.0) + math.pow((((((2.0 * (math.pow(b, 2.0) - math.pow(a, 2.0))) * math.sin(((angle / 180.0) * math.pi))) * math.cos(((angle / 180.0) * math.pi))) / x_45_scale) / y_45_scale), 2.0)))))) / ((4.0 * ((b * a) * (b * -a))) / math.pow((x_45_scale * y_45_scale), 2.0))

↓

def code(a, b, angle, x_45_scale, y_45_scale):
	t_0 = angle * (math.pi * 0.005555555555555556)
	tmp = 0
	if x_45_scale <= -4.0824742066359556e-166:
		tmp = math.hypot((b * math.sin((math.pi * (0.005555555555555556 * angle)))), (a * math.cos(t_0))) * ((x_45_scale * math.pow(16.0, 0.5)) * -0.25)
	elif x_45_scale <= 1.9291306953128207e-163:
		tmp = b * y_45_scale
	else:
		tmp = math.sqrt(2.0) * ((x_45_scale * (math.sqrt(8.0) * math.hypot(a, (b * math.sin(t_0))))) * 0.25)
	return tmp

Julia

function code(a, b, angle, x_45_scale, y_45_scale)
	return Float64(Float64(-sqrt(Float64(Float64(Float64(2.0 * Float64(Float64(4.0 * Float64(Float64(b * a) * Float64(b * Float64(-a)))) / (Float64(x_45_scale * y_45_scale) ^ 2.0))) * Float64(Float64(b * a) * Float64(b * Float64(-a)))) * Float64(Float64(Float64(Float64(Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / x_45_scale) / x_45_scale) + Float64(Float64(Float64((Float64(a * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / y_45_scale) / y_45_scale)) + sqrt(Float64((Float64(Float64(Float64(Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / x_45_scale) / x_45_scale) - Float64(Float64(Float64((Float64(a * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0)) / y_45_scale) / y_45_scale)) ^ 2.0) + (Float64(Float64(Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(Float64(Float64(angle / 180.0) * pi))) * cos(Float64(Float64(angle / 180.0) * pi))) / x_45_scale) / y_45_scale) ^ 2.0))))))) / Float64(Float64(4.0 * Float64(Float64(b * a) * Float64(b * Float64(-a)))) / (Float64(x_45_scale * y_45_scale) ^ 2.0)))
end

↓

function code(a, b, angle, x_45_scale, y_45_scale)
	t_0 = Float64(angle * Float64(pi * 0.005555555555555556))
	tmp = 0.0
	if (x_45_scale <= -4.0824742066359556e-166)
		tmp = Float64(hypot(Float64(b * sin(Float64(pi * Float64(0.005555555555555556 * angle)))), Float64(a * cos(t_0))) * Float64(Float64(x_45_scale * (16.0 ^ 0.5)) * -0.25));
	elseif (x_45_scale <= 1.9291306953128207e-163)
		tmp = Float64(b * y_45_scale);
	else
		tmp = Float64(sqrt(2.0) * Float64(Float64(x_45_scale * Float64(sqrt(8.0) * hypot(a, Float64(b * sin(t_0))))) * 0.25));
	end
	return tmp
end

MATLAB

function tmp = code(a, b, angle, x_45_scale, y_45_scale)
	tmp = -sqrt((((2.0 * ((4.0 * ((b * a) * (b * -a))) / ((x_45_scale * y_45_scale) ^ 2.0))) * ((b * a) * (b * -a))) * (((((((a * sin(((angle / 180.0) * pi))) ^ 2.0) + ((b * cos(((angle / 180.0) * pi))) ^ 2.0)) / x_45_scale) / x_45_scale) + (((((a * cos(((angle / 180.0) * pi))) ^ 2.0) + ((b * sin(((angle / 180.0) * pi))) ^ 2.0)) / y_45_scale) / y_45_scale)) + sqrt(((((((((a * sin(((angle / 180.0) * pi))) ^ 2.0) + ((b * cos(((angle / 180.0) * pi))) ^ 2.0)) / x_45_scale) / x_45_scale) - (((((a * cos(((angle / 180.0) * pi))) ^ 2.0) + ((b * sin(((angle / 180.0) * pi))) ^ 2.0)) / y_45_scale) / y_45_scale)) ^ 2.0) + ((((((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin(((angle / 180.0) * pi))) * cos(((angle / 180.0) * pi))) / x_45_scale) / y_45_scale) ^ 2.0)))))) / ((4.0 * ((b * a) * (b * -a))) / ((x_45_scale * y_45_scale) ^ 2.0));
end

↓

function tmp_2 = code(a, b, angle, x_45_scale, y_45_scale)
	t_0 = angle * (pi * 0.005555555555555556);
	tmp = 0.0;
	if (x_45_scale <= -4.0824742066359556e-166)
		tmp = hypot((b * sin((pi * (0.005555555555555556 * angle)))), (a * cos(t_0))) * ((x_45_scale * (16.0 ^ 0.5)) * -0.25);
	elseif (x_45_scale <= 1.9291306953128207e-163)
		tmp = b * y_45_scale;
	else
		tmp = sqrt(2.0) * ((x_45_scale * (sqrt(8.0) * hypot(a, (b * sin(t_0))))) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := N[((-N[Sqrt[N[(N[(N[(2.0 * N[(N[(4.0 * N[(N[(b * a), $MachinePrecision] * N[(b * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[N[(x$45$scale * y$45$scale), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(b * a), $MachinePrecision] * N[(b * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision] + N[(N[(N[(N[Power[N[(a * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / y$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(N[(N[(N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / x$45$scale), $MachinePrecision] - N[(N[(N[(N[Power[N[(a * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / y$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(N[(N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / x$45$scale), $MachinePrecision] / y$45$scale), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / N[(N[(4.0 * N[(N[(b * a), $MachinePrecision] * N[(b * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[N[(x$45$scale * y$45$scale), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := Block[{t$95$0 = N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$45$scale, -4.0824742066359556e-166], N[(N[Sqrt[N[(b * N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(a * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision] * N[(N[(x$45$scale * N[Power[16.0, 0.5], $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 1.9291306953128207e-163], N[(b * y$45$scale), $MachinePrecision], N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(x$45$scale * N[(N[Sqrt[8.0], $MachinePrecision] * N[Sqrt[a ^ 2 + N[(b * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x-scale < -4.08247420663595555e-166

   1. Initial program 63.4

      \[\frac{-\sqrt{\left(\left(2 \cdot \frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}\right) \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)\right) \cdot \left(\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} + \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right) + \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}\right)}}{\frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}} \]

   2. Taylor expanded in x-scale around inf 60.4

      \[\leadsto \color{blue}{0.25 \cdot \left(\left(y-scale \cdot \left(x-scale \cdot \sqrt{8}\right)\right) \cdot \sqrt{2 \cdot \frac{{a}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{y-scale}^{2}} + 2 \cdot \frac{{b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{y-scale}^{2}}}\right)} \]

   3. Simplified 59.3

      \[\leadsto \color{blue}{\left(0.25 \cdot \left(x-scale \cdot \left(y-scale \cdot \sqrt{8}\right)\right)\right) \cdot \sqrt{2 \cdot \left(\frac{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{y-scale} \cdot \frac{a \cdot a}{y-scale} + \frac{b \cdot b}{y-scale} \cdot \frac{{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{y-scale}\right)}} \]
      Proof
      (*.f64 (*.f64 1/4 (*.f64 x-scale (*.f64 y-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 x-scale y-scale) (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 16 points increase in error, 8 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (sqrt.f64 8))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (Rewrite<= associate-*r*_binary64 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8))))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 6 points increase in error, 17 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (pow.f64 a 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 17 points increase in error, 7 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 y-scale y-scale))))))): 5 points increase in error, 7 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))) (*.f64 2 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 1/4 (*.f64 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))) (*.f64 2 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)))))))): 1 points increase in error, 0 points decrease in error

   4. Taylor expanded in y-scale around -inf 48.0

      \[\leadsto \color{blue}{-0.25 \cdot \left(\left(\sqrt{2} \cdot \left(x-scale \cdot \sqrt{8}\right)\right) \cdot \sqrt{{a}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + {b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}\right)} \]

   5. Simplified 38.1

      \[\leadsto \color{blue}{\mathsf{hypot}\left(b \cdot \sin \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right), a \cdot \cos \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)\right) \cdot \left(\left(\sqrt{2} \cdot \left(x-scale \cdot \sqrt{8}\right)\right) \cdot -0.25\right)} \]
      Proof
      (*.f64 (hypot.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 1/180 (PI.f64)) angle))) (*.f64 a (cos.f64 (*.f64 (*.f64 1/180 (PI.f64)) angle)))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (hypot.f64 (*.f64 b (sin.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/180 (*.f64 (PI.f64) angle))))) (*.f64 a (cos.f64 (*.f64 (*.f64 1/180 (PI.f64)) angle)))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 14 points increase in error, 8 points decrease in error
      (*.f64 (hypot.f64 (*.f64 b (sin.f64 (*.f64 1/180 (Rewrite<= *-commutative_binary64 (*.f64 angle (PI.f64)))))) (*.f64 a (cos.f64 (*.f64 (*.f64 1/180 (PI.f64)) angle)))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (hypot.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/180 (*.f64 (PI.f64) angle)))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 4 points increase in error, 6 points decrease in error
      (*.f64 (hypot.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (*.f64 1/180 (Rewrite<= *-commutative_binary64 (*.f64 angle (PI.f64))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (*.f64 (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 64 points increase in error, 10 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 b b) (*.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))))) (*.f64 (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 18 points increase in error, 7 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (*.f64 (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) (*.f64 (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 a (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 a a) (*.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 4 points increase in error, 3 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (pow.f64 a 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) -1/4)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)))) (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8)))) -1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)))))) -1/4): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 -1/4 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))))))): 0 points increase in error, 0 points decrease in error

   6. Applied egg-rr 37.8

      \[\leadsto \mathsf{hypot}\left(b \cdot \sin \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right), a \cdot \cos \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)\right) \cdot \left(\color{blue}{\left(0 + x-scale \cdot {16}^{0.5}\right)} \cdot -0.25\right) \]

   7. Taylor expanded in angle around inf 37.9

      \[\leadsto \mathsf{hypot}\left(b \cdot \color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}, a \cdot \cos \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)\right) \cdot \left(\left(0 + x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right) \]

   8. Simplified 37.8

      \[\leadsto \mathsf{hypot}\left(b \cdot \color{blue}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}, a \cdot \cos \left(\left(0.005555555555555556 \cdot \pi\right) \cdot angle\right)\right) \cdot \left(\left(0 + x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right) \]
      Proof
      (sin.f64 (*.f64 (PI.f64) (*.f64 1/180 angle))): 0 points increase in error, 0 points decrease in error
      (sin.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 1/180 angle) (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (sin.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/180 (*.f64 angle (PI.f64))))): 51 points increase in error, 46 points decrease in error

   if -4.08247420663595555e-166 < x-scale < 1.92913069531282073e-163

   1. Initial program 63.9

      \[\frac{-\sqrt{\left(\left(2 \cdot \frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}\right) \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)\right) \cdot \left(\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} + \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right) + \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}\right)}}{\frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}} \]

   2. Simplified 64.0

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{8 \cdot \left(\left(b \cdot \left(a \cdot \left(b \cdot a\right)\right)\right) \cdot \left(b \cdot \left(a \cdot \left(b \cdot a\right)\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}} \cdot \left(\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale} + \left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} + \mathsf{hypot}\left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{\frac{2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)}{\frac{x-scale}{b \cdot b - a \cdot a}}}{\frac{y-scale}{\cos \left(\frac{angle}{180} \cdot \pi\right)}}\right)\right)\right)}}{b \cdot \left(\left(b \cdot a\right) \cdot \left(a \cdot -4\right)\right)} \cdot \left(-{\left(x-scale \cdot y-scale\right)}^{2}\right)} \]
      Proof
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 8 (*.f64 (*.f64 b (*.f64 a (*.f64 b a))) (*.f64 b (*.f64 a (*.f64 b a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 4 2)) (*.f64 (*.f64 b (*.f64 a (*.f64 b a))) (*.f64 b (*.f64 a (*.f64 b a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 b a) (*.f64 b a))) (*.f64 b (*.f64 a (*.f64 b a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 b a) b) a)) (*.f64 b (*.f64 a (*.f64 b a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (*.f64 (*.f64 (*.f64 b a) b) a) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 b a) (*.f64 b a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (*.f64 (*.f64 (*.f64 b a) b) a) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 b a) b) a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (Rewrite<= sqr-neg_binary64 (*.f64 (neg.f64 (*.f64 (*.f64 (*.f64 b a) b) a)) (neg.f64 (*.f64 (*.f64 (*.f64 b a) b) a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (Rewrite<= distribute-rgt-neg-out_binary64 (*.f64 (*.f64 (*.f64 b a) b) (neg.f64 a))) (neg.f64 (*.f64 (*.f64 (*.f64 b a) b) a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (neg.f64 (*.f64 (*.f64 (*.f64 b a) b) a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (Rewrite<= distribute-rgt-neg-out_binary64 (*.f64 (*.f64 (*.f64 b a) b) (neg.f64 a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 4 2) (*.f64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))) (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 1 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 4 2) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (Rewrite=> metadata-eval 8) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 2 4)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (*.f64 2 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))) (pow.f64 (*.f64 x-scale y-scale) 2)) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (Rewrite<= associate-*r/_binary64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (/.f64 (/.f64 (*.f64 2 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 2)) (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (/.f64 (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 2) (/.f64 x-scale (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a)))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (/.f64 (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 2) (/.f64 x-scale (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2))))) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 2) (-.f64 (pow.f64 b 2) (pow.f64 a 2))) x-scale)) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 1 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))))) x-scale) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) x-scale) (/.f64 y-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (/.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) y-scale))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (/.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale)) y-scale)))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale))))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 6 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2)) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2))))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 a (Rewrite<= metadata-eval (*.f64 -1 4)))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 a -1) 4))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 a)) 4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (*.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 a)) 4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (*.f64 b a) (Rewrite=> *-commutative_binary64 (*.f64 4 (neg.f64 a)))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 b a) 4) (neg.f64 a))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 b a))) (neg.f64 a)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 b (Rewrite=> *-commutative_binary64 (*.f64 (neg.f64 a) (*.f64 4 (*.f64 b a)))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 b (neg.f64 a)) (*.f64 4 (*.f64 b a))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 1 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 4 (*.f64 b a)) (*.f64 b (neg.f64 a))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (Rewrite<= associate-*r*_binary64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a))))) (pow.f64 (*.f64 x-scale y-scale) 2)))): 0 points increase in error, 0 points decrease in error
      (neg.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2)))))) (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))))): 2 points increase in error, 1 points decrease in error
      (Rewrite<= distribute-frac-neg_binary64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 2 (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (+.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2))))))) (/.f64 (*.f64 4 (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in angle around 0 49.6

      \[\leadsto \color{blue}{0.25 \cdot \left(y-scale \cdot \left(\sqrt{2} \cdot \left(b \cdot \sqrt{8}\right)\right)\right)} \]

   4. Simplified 49.6

      \[\leadsto \color{blue}{0.25 \cdot \left(y-scale \cdot \left(\left(\sqrt{8} \cdot b\right) \cdot \sqrt{2}\right)\right)} \]
      Proof
      (*.f64 1/4 (*.f64 y-scale (*.f64 (*.f64 (sqrt.f64 8) b) (sqrt.f64 2)))): 0 points increase in error, 0 points decrease in error
      (*.f64 1/4 (*.f64 y-scale (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 b (sqrt.f64 8))) (sqrt.f64 2)))): 0 points increase in error, 0 points decrease in error
      (*.f64 1/4 (*.f64 y-scale (Rewrite<= *-commutative_binary64 (*.f64 (sqrt.f64 2) (*.f64 b (sqrt.f64 8)))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 49.4

      \[\leadsto 0.25 \cdot \left(y-scale \cdot \color{blue}{\left(0 + b \cdot {16}^{0.5}\right)}\right) \]

   6. Taylor expanded in y-scale around 0 49.4

      \[\leadsto \color{blue}{y-scale \cdot b} \]

   if 1.92913069531282073e-163 < x-scale

   1. Initial program 63.2

      \[\frac{-\sqrt{\left(\left(2 \cdot \frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}\right) \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)\right) \cdot \left(\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} + \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right) + \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}\right)}}{\frac{4 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot \left(-a\right)\right)\right)}{{\left(x-scale \cdot y-scale\right)}^{2}}} \]

   2. Taylor expanded in x-scale around inf 60.5

      \[\leadsto \color{blue}{0.25 \cdot \left(\left(y-scale \cdot \left(x-scale \cdot \sqrt{8}\right)\right) \cdot \sqrt{2 \cdot \frac{{a}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{y-scale}^{2}} + 2 \cdot \frac{{b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{y-scale}^{2}}}\right)} \]

   3. Simplified 59.7

      \[\leadsto \color{blue}{\left(0.25 \cdot \left(x-scale \cdot \left(y-scale \cdot \sqrt{8}\right)\right)\right) \cdot \sqrt{2 \cdot \left(\frac{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{y-scale} \cdot \frac{a \cdot a}{y-scale} + \frac{b \cdot b}{y-scale} \cdot \frac{{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{y-scale}\right)}} \]
      Proof
      (*.f64 (*.f64 1/4 (*.f64 x-scale (*.f64 y-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 x-scale y-scale) (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 16 points increase in error, 8 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 y-scale x-scale)) (sqrt.f64 8))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (Rewrite<= associate-*r*_binary64 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8))))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (*.f64 a a) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 6 points increase in error, 17 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (pow.f64 a 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 17 points increase in error, 7 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))) (*.f64 (/.f64 (*.f64 b b) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) y-scale) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) y-scale)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (*.f64 y-scale y-scale))))))): 5 points increase in error, 7 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)) (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (Rewrite<= unpow2_binary64 (pow.f64 y-scale 2))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 1/4 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8)))) (sqrt.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))) (*.f64 2 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 1/4 (*.f64 (*.f64 y-scale (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2))) (*.f64 2 (/.f64 (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)) (pow.f64 y-scale 2)))))))): 1 points increase in error, 0 points decrease in error

   4. Taylor expanded in angle around 0 59.7

      \[\leadsto \left(0.25 \cdot \left(x-scale \cdot \left(y-scale \cdot \sqrt{8}\right)\right)\right) \cdot \sqrt{2 \cdot \left(\frac{{\color{blue}{1}}^{2}}{y-scale} \cdot \frac{a \cdot a}{y-scale} + \frac{b \cdot b}{y-scale} \cdot \frac{{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{y-scale}\right)} \]

   5. Taylor expanded in y-scale around 0 47.4

      \[\leadsto \color{blue}{0.25 \cdot \left(\left(\sqrt{2} \cdot \left(x-scale \cdot \sqrt{8}\right)\right) \cdot \sqrt{{a}^{2} + {b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}\right)} \]

   6. Simplified 36.9

      \[\leadsto \color{blue}{\sqrt{2} \cdot \left(\left(x-scale \cdot \left(\sqrt{8} \cdot \mathsf{hypot}\left(a, b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right) \cdot 0.25\right)} \]
      Proof
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (hypot.f64 a (*.f64 b (sin.f64 (*.f64 angle (*.f64 (PI.f64) 1/180))))))) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (hypot.f64 a (*.f64 b (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle (PI.f64)) 1/180))))))) 1/4)): 12 points increase in error, 9 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (hypot.f64 a (*.f64 b (sin.f64 (Rewrite<= *-commutative_binary64 (*.f64 1/180 (*.f64 angle (PI.f64))))))))) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))))))))) 1/4)): 64 points increase in error, 10 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) (*.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))))) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (sqrt.f64 (+.f64 (pow.f64 a 2) (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 b b) (*.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))))))))) 1/4)): 18 points increase in error, 5 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))))) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (*.f64 (sqrt.f64 8) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))))))) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)))))) 1/4)): 19 points increase in error, 17 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)))))) 1/4)): 1 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2)))))) 1/4): 27 points increase in error, 22 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 1/4 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 x-scale (sqrt.f64 8))) (sqrt.f64 (+.f64 (pow.f64 a 2) (*.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 40.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\mathsf{hypot}\left(b \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right), a \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right) \cdot \left(\left(x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\left(x-scale \cdot \left(\sqrt{8} \cdot \mathsf{hypot}\left(a, b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right) \cdot 0.25\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	40.5
Cost	33224

\[\begin{array}{l} t_0 := b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\\ \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right) \cdot \mathsf{hypot}\left(t_0, a\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\left(x-scale \cdot \left(\sqrt{8} \cdot \mathsf{hypot}\left(a, t_0\right)\right)\right) \cdot 0.25\right)\\ \end{array} \]

Alternative 2
Error	40.6
Cost	33224

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\mathsf{hypot}\left(b \cdot \sin t_0, a \cdot \cos t_0\right) \cdot \left(-x-scale\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\left(x-scale \cdot \left(\sqrt{8} \cdot \mathsf{hypot}\left(a, b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right) \cdot 0.25\right)\\ \end{array} \]

Alternative 3
Error	48.5
Cost	26696

\[\begin{array}{l} \mathbf{if}\;x-scale \leq -5.168873598207093 \cdot 10^{-152}:\\ \;\;\;\;x-scale \cdot \left(-a\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(\left(x-scale \cdot \sqrt{8}\right) \cdot \mathsf{hypot}\left(a, a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 4
Error	44.2
Cost	26696

\[\begin{array}{l} t_0 := x-scale \cdot \sqrt{8}\\ \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\mathsf{hypot}\left(b \cdot \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right), a\right) \cdot \left(-0.25 \cdot \left(\sqrt{2} \cdot t_0\right)\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(t_0 \cdot \mathsf{hypot}\left(a, a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	43.1
Cost	26696

\[\begin{array}{l} \mathbf{if}\;x-scale \leq -4.0824742066359556 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(x-scale \cdot {16}^{0.5}\right) \cdot -0.25\right) \cdot \mathsf{hypot}\left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right), a\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(\left(x-scale \cdot \sqrt{8}\right) \cdot \mathsf{hypot}\left(a, a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 6
Error	51.7
Cost	13708

\[\begin{array}{l} t_0 := x-scale \cdot \left(-a\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq -2.10643477570692 \cdot 10^{-77}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{elif}\;a \leq 1.432076936476363 \cdot 10^{-233}:\\ \;\;\;\;\sqrt{{\left(y-scale \cdot \left(b \cdot 4\right)\right)}^{2} \cdot 0.0625}\\ \mathbf{elif}\;a \leq 3.4510363911739912 \cdot 10^{-93}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	51.7
Cost	13640

\[\begin{array}{l} \mathbf{if}\;x-scale \leq -5.168873598207093 \cdot 10^{-152}:\\ \;\;\;\;x-scale \cdot \left(-a\right)\\ \mathbf{elif}\;x-scale \leq 5.995194863903718 \cdot 10^{-137}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(\sqrt{2} \cdot \left(x-scale \cdot \left(a \cdot \sqrt{8}\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	51.7
Cost	13640

\[\begin{array}{l} \mathbf{if}\;x-scale \leq -5.168873598207093 \cdot 10^{-152}:\\ \;\;\;\;x-scale \cdot \left(-a\right)\\ \mathbf{elif}\;x-scale \leq 5.995194863903718 \cdot 10^{-137}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(\left(x-scale \cdot \sqrt{8}\right) \cdot \left(a \cdot \sqrt{2}\right)\right)\\ \end{array} \]

Alternative 9
Error	51.9
Cost	13576

\[\begin{array}{l} \mathbf{if}\;x-scale \leq -5.168873598207093 \cdot 10^{-152}:\\ \;\;\;\;x-scale \cdot \left(-a\right)\\ \mathbf{elif}\;x-scale \leq 1.9291306953128207 \cdot 10^{-163}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;x-scale \cdot \left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	52.7
Cost	7500

\[\begin{array}{l} t_0 := x-scale \cdot \left(-a\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq -2.10643477570692 \cdot 10^{-77}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{elif}\;a \leq -1.0910892546684247 \cdot 10^{-190}:\\ \;\;\;\;0.25 \cdot \left(y-scale \cdot \sqrt{2 \cdot \left(8 \cdot \left(b \cdot b\right)\right)}\right)\\ \mathbf{elif}\;a \leq 3.4510363911739912 \cdot 10^{-93}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	52.3
Cost	520

\[\begin{array}{l} t_0 := x-scale \cdot \left(-a\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 3.4510363911739912 \cdot 10^{-93}:\\ \;\;\;\;b \cdot y-scale\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	54.4
Cost	192

\[b \cdot y-scale \]

Reproduce

herbie shell --seed 2022320 
(FPCore (a b angle x-scale y-scale)
  :name "a from scale-rotated-ellipse"
  :precision binary64
  (/ (- (sqrt (* (* (* 2.0 (/ (* 4.0 (* (* b a) (* b (- a)))) (pow (* x-scale y-scale) 2.0))) (* (* b a) (* b (- a)))) (+ (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180.0) PI))) 2.0) (pow (* b (sin (* (/ angle 180.0) PI))) 2.0)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180.0) PI))) 2.0) (pow (* b (sin (* (/ angle 180.0) PI))) 2.0)) y-scale) y-scale)) 2.0) (pow (/ (/ (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI))) (cos (* (/ angle 180.0) PI))) x-scale) y-scale) 2.0))))))) (/ (* 4.0 (* (* b a) (* b (- a)))) (pow (* x-scale y-scale) 2.0))))