raw-angle from scale-rotated-ellipse

Average Error: 55.4 → 53.5

Time: 1.9min

Precision: binary64

Cost: 232256

Math

\[180 \cdot \frac{\tan^{-1} \left(\frac{\left(\frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} - \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) - \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}}{\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}}\right)}{\pi} \]

↓

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ t_1 := \cos t_0\\ t_2 := \sin t_0\\ t_3 := \frac{{\left(t_1 \cdot a\right)}^{2} + {\left(t_2 \cdot b\right)}^{2}}{y-scale \cdot y-scale}\\ t_4 := \frac{{\left(a \cdot t_2\right)}^{2} + {\left(t_1 \cdot b\right)}^{2}}{x-scale \cdot x-scale}\\ 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(y-scale \cdot \frac{\left(t_3 - t_4\right) - \mathsf{hypot}\left(t_4 - t_3, 2 \cdot \left(t_2 \cdot \left(\frac{a + b}{x-scale} \cdot \frac{t_1 \cdot \left(b - a\right)}{y-scale}\right)\right)\right)}{t_1 \cdot \left(t_2 \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)\right)}{\pi} \end{array} \]

FPCore

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

↓

(FPCore (a b angle x-scale y-scale)
 :precision binary64
 (let* ((t_0 (* angle (* 0.005555555555555556 PI)))
        (t_1 (cos t_0))
        (t_2 (sin t_0))
        (t_3
         (/ (+ (pow (* t_1 a) 2.0) (pow (* t_2 b) 2.0)) (* y-scale y-scale)))
        (t_4
         (/ (+ (pow (* a t_2) 2.0) (pow (* t_1 b) 2.0)) (* x-scale x-scale))))
   (*
    180.0
    (/
     (atan
      (*
       x-scale
       (*
        y-scale
        (/
         (-
          (- t_3 t_4)
          (hypot
           (- t_4 t_3)
           (*
            2.0
            (* t_2 (* (/ (+ a b) x-scale) (/ (* t_1 (- b a)) y-scale))))))
         (* t_1 (* t_2 (* 2.0 (* (+ a b) (- b a)))))))))
     PI))))

C

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return 180.0 * (atan(((((((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) - (((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)) - 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)))) / (((((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))) / ((double) M_PI));
}

↓

double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = angle * (0.005555555555555556 * ((double) M_PI));
	double t_1 = cos(t_0);
	double t_2 = sin(t_0);
	double t_3 = (pow((t_1 * a), 2.0) + pow((t_2 * b), 2.0)) / (y_45_scale * y_45_scale);
	double t_4 = (pow((a * t_2), 2.0) + pow((t_1 * b), 2.0)) / (x_45_scale * x_45_scale);
	return 180.0 * (atan((x_45_scale * (y_45_scale * (((t_3 - t_4) - hypot((t_4 - t_3), (2.0 * (t_2 * (((a + b) / x_45_scale) * ((t_1 * (b - a)) / y_45_scale)))))) / (t_1 * (t_2 * (2.0 * ((a + b) * (b - a))))))))) / ((double) M_PI));
}

Java

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	return 180.0 * (Math.atan(((((((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.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.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)))) / (((((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))) / Math.PI);
}

↓

public static double code(double a, double b, double angle, double x_45_scale, double y_45_scale) {
	double t_0 = angle * (0.005555555555555556 * Math.PI);
	double t_1 = Math.cos(t_0);
	double t_2 = Math.sin(t_0);
	double t_3 = (Math.pow((t_1 * a), 2.0) + Math.pow((t_2 * b), 2.0)) / (y_45_scale * y_45_scale);
	double t_4 = (Math.pow((a * t_2), 2.0) + Math.pow((t_1 * b), 2.0)) / (x_45_scale * x_45_scale);
	return 180.0 * (Math.atan((x_45_scale * (y_45_scale * (((t_3 - t_4) - Math.hypot((t_4 - t_3), (2.0 * (t_2 * (((a + b) / x_45_scale) * ((t_1 * (b - a)) / y_45_scale)))))) / (t_1 * (t_2 * (2.0 * ((a + b) * (b - a))))))))) / Math.PI);
}

Python

def code(a, b, angle, x_45_scale, y_45_scale):
	return 180.0 * (math.atan(((((((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.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.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)))) / (((((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))) / math.pi)

↓

def code(a, b, angle, x_45_scale, y_45_scale):
	t_0 = angle * (0.005555555555555556 * math.pi)
	t_1 = math.cos(t_0)
	t_2 = math.sin(t_0)
	t_3 = (math.pow((t_1 * a), 2.0) + math.pow((t_2 * b), 2.0)) / (y_45_scale * y_45_scale)
	t_4 = (math.pow((a * t_2), 2.0) + math.pow((t_1 * b), 2.0)) / (x_45_scale * x_45_scale)
	return 180.0 * (math.atan((x_45_scale * (y_45_scale * (((t_3 - t_4) - math.hypot((t_4 - t_3), (2.0 * (t_2 * (((a + b) / x_45_scale) * ((t_1 * (b - a)) / y_45_scale)))))) / (t_1 * (t_2 * (2.0 * ((a + b) * (b - a))))))))) / math.pi)

Julia

function code(a, b, angle, x_45_scale, y_45_scale)
	return Float64(180.0 * Float64(atan(Float64(Float64(Float64(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) - 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)) - 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(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))) / pi))
end

↓

function code(a, b, angle, x_45_scale, y_45_scale)
	t_0 = Float64(angle * Float64(0.005555555555555556 * pi))
	t_1 = cos(t_0)
	t_2 = sin(t_0)
	t_3 = Float64(Float64((Float64(t_1 * a) ^ 2.0) + (Float64(t_2 * b) ^ 2.0)) / Float64(y_45_scale * y_45_scale))
	t_4 = Float64(Float64((Float64(a * t_2) ^ 2.0) + (Float64(t_1 * b) ^ 2.0)) / Float64(x_45_scale * x_45_scale))
	return Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(y_45_scale * Float64(Float64(Float64(t_3 - t_4) - hypot(Float64(t_4 - t_3), Float64(2.0 * Float64(t_2 * Float64(Float64(Float64(a + b) / x_45_scale) * Float64(Float64(t_1 * Float64(b - a)) / y_45_scale)))))) / Float64(t_1 * Float64(t_2 * Float64(2.0 * Float64(Float64(a + b) * Float64(b - a))))))))) / pi))
end

MATLAB

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

↓

function tmp = code(a, b, angle, x_45_scale, y_45_scale)
	t_0 = angle * (0.005555555555555556 * pi);
	t_1 = cos(t_0);
	t_2 = sin(t_0);
	t_3 = (((t_1 * a) ^ 2.0) + ((t_2 * b) ^ 2.0)) / (y_45_scale * y_45_scale);
	t_4 = (((a * t_2) ^ 2.0) + ((t_1 * b) ^ 2.0)) / (x_45_scale * x_45_scale);
	tmp = 180.0 * (atan((x_45_scale * (y_45_scale * (((t_3 - t_4) - hypot((t_4 - t_3), (2.0 * (t_2 * (((a + b) / x_45_scale) * ((t_1 * (b - a)) / y_45_scale)))))) / (t_1 * (t_2 * (2.0 * ((a + b) * (b - a))))))))) / pi);
end

Wolfram

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := N[(180.0 * N[(N[ArcTan[N[(N[(N[(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] - 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]), $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] / 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]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_, x$45$scale_, y$45$scale_] := Block[{t$95$0 = N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Power[N[(t$95$1 * a), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(t$95$2 * b), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(y$45$scale * y$45$scale), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[Power[N[(a * t$95$2), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(t$95$1 * b), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(x$45$scale * x$45$scale), $MachinePrecision]), $MachinePrecision]}, N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(y$45$scale * N[(N[(N[(t$95$3 - t$95$4), $MachinePrecision] - N[Sqrt[N[(t$95$4 - t$95$3), $MachinePrecision] ^ 2 + N[(2.0 * N[(t$95$2 * N[(N[(N[(a + b), $MachinePrecision] / x$45$scale), $MachinePrecision] * N[(N[(t$95$1 * N[(b - a), $MachinePrecision]), $MachinePrecision] / y$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * N[(t$95$2 * N[(2.0 * N[(N[(a + b), $MachinePrecision] * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 55.4

   \[180 \cdot \frac{\tan^{-1} \left(\frac{\left(\frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale} - \frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale}\right) - \sqrt{{\left(\frac{\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{x-scale}}{x-scale} - \frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale}}{y-scale}\right)}^{2} + {\left(\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}\right)}^{2}}}{\frac{\frac{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)}{x-scale}}{y-scale}}\right)}{\pi} \]

2. Simplified 55.5

   \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale} - \left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} + \sqrt{{\left(\frac{{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(a \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}\right)}^{2} + {\left(\frac{\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale \cdot x-scale}\right)}^{2}}\right)}{\frac{\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale \cdot x-scale}}\right)}{\pi}} \]
   Proof
   (*.f64 180 (/.f64 (atan.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)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 2 points increase in error, 7 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (Rewrite<= *-commutative_binary64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))))) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) b) 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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (Rewrite<= *-commutative_binary64 (*.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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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) (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))) 2) (pow.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 4 points increase in error, 2 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2)))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (Rewrite<= *-commutative_binary64 (*.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))))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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 (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)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) 2))))) (/.f64 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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 (+.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<= remove-double-neg_binary64 (neg.f64 (neg.f64 (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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.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) (Rewrite<= sub-neg_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) (neg.f64 (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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (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)) (neg.f64 (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 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (Rewrite<= sub-neg_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 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 b 2)) (*.f64 a a))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 2 (-.f64 (pow.f64 b 2) (Rewrite<= unpow2_binary64 (pow.f64 a 2)))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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 (*.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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 (Rewrite<= *-commutative_binary64 (*.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))))) (*.f64 y-scale x-scale)))) (PI.f64))): 0 points increase in error, 0 points decrease in error
   (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.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)))) (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)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)))) (PI.f64))): 5 points increase in error, 6 points decrease in error

3. Applied egg-rr 57.3

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{\frac{{\left(a \cdot \cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}}{\frac{\left(\cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right) \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)}{y-scale \cdot x-scale}} - \frac{\frac{{\left(a \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2} + {\left(\cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} + \sqrt{{\left(\frac{{\left(a \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2} + {\left(\cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(a \cdot \cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right)}^{2}}{y-scale \cdot y-scale}\right)}^{2} + {\left(\frac{\left(\cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right) \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)}{y-scale \cdot x-scale}\right)}^{2}}}{\frac{\left(\cos \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right) \cdot \sin \left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)}{y-scale \cdot x-scale}}\right)}}{\pi} \]

4. Simplified 53.5

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(x-scale \cdot \frac{\left(\left(\frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{y-scale \cdot y-scale} - \frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale}\right) - \mathsf{hypot}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(a \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}}{y-scale \cdot y-scale}, \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{\frac{y-scale}{\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}} \cdot \frac{\left(a + b\right) \cdot \left(b - a\right)}{\frac{x-scale}{2}}\right)\right) \cdot y-scale}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)}}{\pi} \]
   Proof
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 2 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 2 points increase in error, 1 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 2 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 2 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (/.f64 y-scale (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (/.f64 y-scale (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 1 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale)) (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale) (/.f64 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 b a)) (-.f64 b a)) (/.f64 x-scale 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) 2) x-scale))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) y-scale) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) x-scale)))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 2 points increase in error, 2 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)))) (*.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale))))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 15 points increase in error, 3 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2)) (*.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (Rewrite<= associate--r+_binary64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2)))))) y-scale) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) y-scale) (*.f64 (cos.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 1 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) y-scale) (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (*.f64 (sin.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) y-scale) (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (*.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (*.f64 2 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 b a)) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 x-scale (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) y-scale) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a))))))): 0 points increase in error, 2 points decrease in error
   (*.f64 x-scale (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a))))) y-scale))): 4 points increase in error, 3 points decrease in error
   (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a))))) y-scale) x-scale)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a))))) (*.f64 y-scale x-scale))): 15 points increase in error, 5 points decrease in error
   (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2))))) (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)))): 5 points increase in error, 1 points decrease in error
   (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale))) (/.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) 2) (pow.f64 (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale)) 2)))) (/.f64 (*.f64 (*.f64 (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))) (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 2 (*.f64 (+.f64 b a) (-.f64 b a)))) (*.f64 y-scale x-scale))))): 0 points increase in error, 0 points decrease in error

5. Applied egg-rr 53.6

   \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \color{blue}{\left(\left(y-scale \cdot \left(\frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale} - \left(\frac{{\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} + \mathsf{hypot}\left(\frac{{\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale}, \left(\frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale} \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right) \cdot \left(\frac{\left(a + b\right) \cdot \left(b - a\right)}{x-scale} \cdot 2\right)\right)\right)\right)\right) \cdot \frac{1}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)}\right)}{\pi} \]

6. Simplified 53.5

   \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \color{blue}{\left(y-scale \cdot \frac{\left(\frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale} - \frac{{\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale}\right) - \mathsf{hypot}\left(\frac{{\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale}, \left(\left(2 \cdot \left(\frac{a + b}{x-scale} \cdot \left(b - a\right)\right)\right) \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right) \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)}\right)}{\pi} \]
   Proof
   (*.f64 y-scale (/.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 (+.f64 a b) x-scale) (-.f64 b a))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale)) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (/.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (*.f64 2 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale))) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale)) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (/.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2)) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale)) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (/.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2) (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 1 points increase in error, 1 points decrease in error
   (*.f64 y-scale (/.f64 (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2)))))) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))): 0 points increase in error, 1 points decrease in error
   (*.f64 y-scale (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2))))) (Rewrite<= /-rgt-identity_binary64 (/.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))) 1)))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2))))) 1) (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a)))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 y-scale (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2))))) (/.f64 1 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a))))))))): 2 points increase in error, 1 points decrease in error
   (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y-scale (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) (*.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 b a)) x-scale) 2)))))) (/.f64 1 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (+.f64 a b) (-.f64 b a)))))))): 3 points increase in error, 7 points decrease in error

7. Applied egg-rr 53.5

   \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(y-scale \cdot \frac{\color{blue}{\left(\frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale} - \frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale}\right) + \left(-\mathsf{hypot}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale}, \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(\frac{a + b}{x-scale} \cdot \left(b - a\right)\right) \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right)\right)\right)\right)}}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)\right)}{\pi} \]

8. Simplified 53.5

   \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(y-scale \cdot \frac{\color{blue}{\left(\frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale} - \frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale}\right) - \mathsf{hypot}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale}, 2 \cdot \left(\left(\frac{a + b}{x-scale} \cdot \frac{\left(b - a\right) \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}{y-scale}\right) \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)}}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)\right)}{\pi} \]
   Proof
   (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 2 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (/.f64 (*.f64 (-.f64 b a) (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) y-scale)) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
   (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 2 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 b a) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale)))) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))))): 3 points increase in error, 1 points decrease in error
   (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 2 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (-.f64 b a)) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))))): 2 points increase in error, 0 points decrease in error
   (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (-.f64 b a)) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))) (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
   (-.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (Rewrite<= *-commutative_binary64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (-.f64 b a)) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale))))))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= unsub-neg_binary64 (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale))) (neg.f64 (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64))))) 2) (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) a) 2) (pow.f64 (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) b) 2)) (*.f64 y-scale y-scale))) (*.f64 (sin.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) (*.f64 2 (*.f64 (*.f64 (/.f64 (+.f64 a b) x-scale) (-.f64 b a)) (/.f64 (cos.f64 (*.f64 angle (*.f64 1/180 (PI.f64)))) y-scale)))))))): 0 points increase in error, 0 points decrease in error

9. Final simplification 53.5

   \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(y-scale \cdot \frac{\left(\frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale} - \frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale}\right) - \mathsf{hypot}\left(\frac{{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{x-scale \cdot x-scale} - \frac{{\left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot a\right)}^{2} + {\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot b\right)}^{2}}{y-scale \cdot y-scale}, 2 \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\frac{a + b}{x-scale} \cdot \frac{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(b - a\right)}{y-scale}\right)\right)\right)}{\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)}\right)\right)}{\pi} \]

Reproduce

herbie shell --seed 2022334 
(FPCore (a b angle x-scale y-scale)
  :name "raw-angle from scale-rotated-ellipse"
  :precision binary64
  (* 180.0 (/ (atan (/ (- (- (/ (/ (+ (pow (* a (cos (* (/ angle 180.0) PI))) 2.0) (pow (* b (sin (* (/ angle 180.0) PI))) 2.0)) y-scale) y-scale) (/ (/ (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)) x-scale) x-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)))) (/ (/ (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* (/ angle 180.0) PI))) (cos (* (/ angle 180.0) PI))) x-scale) y-scale))) PI)))