raw-angle from scale-rotated-ellipse

Average Accuracy: 14.0% → 54.8%

Time: 2.4min

Precision: binary64

Cost: 118860

Math

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

↓

\[\begin{array}{l} t_0 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ t_1 := \sin t_0\\ t_2 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ t_3 := \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{t_1}{\frac{\cos t_0}{x-scale}}}\right)\right) \cdot \frac{180}{\pi}\\ t_4 := \sin t_2\\ t_5 := \sqrt[3]{0.005555555555555556 \cdot angle}\\ t_6 := \cos t_2\\ t_7 := {\left(b \cdot t_6\right)}^{2}\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{t_4}{\cos \left({t_5}^{2} \cdot \left(\pi \cdot t_5\right)\right)}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;b \leq 122000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \sqrt{{\left(\frac{t_7 + \mathsf{fma}\left(2, {\left(t_4 \cdot a\right)}^{2}, t_7\right)}{t_6 \cdot \left(t_4 \cdot \left(b \cdot b - a \cdot a\right)\right)}\right)}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \left(\pi \cdot \left(angle \cdot \log \left(e^{0.005555555555555556}\right)\right)\right)} \cdot \frac{t_1}{x-scale}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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 (* PI (* 0.005555555555555556 angle)))
        (t_1 (sin t_0))
        (t_2 (* 0.005555555555555556 (* PI angle)))
        (t_3
         (*
          (atan (* y-scale (* -0.5 (/ 2.0 (/ t_1 (/ (cos t_0) x-scale))))))
          (/ 180.0 PI)))
        (t_4 (sin t_2))
        (t_5 (cbrt (* 0.005555555555555556 angle)))
        (t_6 (cos t_2))
        (t_7 (pow (* b t_6) 2.0)))
   (if (<= b -1.05e+41)
     t_3
     (if (<= b 2.05e-100)
       (*
        180.0
        (/
         (atan
          (*
           -0.5
           (*
            (/ y-scale x-scale)
            (* -2.0 (/ t_4 (cos (* (pow t_5 2.0) (* PI t_5))))))))
         PI))
       (if (<= b 122000.0)
         (*
          180.0
          (/
           (atan
            (*
             -0.5
             (*
              (/ y-scale x-scale)
              (sqrt
               (pow
                (/
                 (+ t_7 (fma 2.0 (pow (* t_4 a) 2.0) t_7))
                 (* t_6 (* t_4 (- (* b b) (* a a)))))
                2.0)))))
           PI))
         (if (<= b 3.2e+157)
           (*
            (/ 180.0 PI)
            (atan
             (*
              y-scale
              (*
               -0.5
               (*
                (/
                 -2.0
                 (cos (* PI (* angle (log (exp 0.005555555555555556))))))
                (/ t_1 x-scale))))))
           t_3))))))

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 = ((double) M_PI) * (0.005555555555555556 * angle);
	double t_1 = sin(t_0);
	double t_2 = 0.005555555555555556 * (((double) M_PI) * angle);
	double t_3 = atan((y_45_scale * (-0.5 * (2.0 / (t_1 / (cos(t_0) / x_45_scale)))))) * (180.0 / ((double) M_PI));
	double t_4 = sin(t_2);
	double t_5 = cbrt((0.005555555555555556 * angle));
	double t_6 = cos(t_2);
	double t_7 = pow((b * t_6), 2.0);
	double tmp;
	if (b <= -1.05e+41) {
		tmp = t_3;
	} else if (b <= 2.05e-100) {
		tmp = 180.0 * (atan((-0.5 * ((y_45_scale / x_45_scale) * (-2.0 * (t_4 / cos((pow(t_5, 2.0) * (((double) M_PI) * t_5)))))))) / ((double) M_PI));
	} else if (b <= 122000.0) {
		tmp = 180.0 * (atan((-0.5 * ((y_45_scale / x_45_scale) * sqrt(pow(((t_7 + fma(2.0, pow((t_4 * a), 2.0), t_7)) / (t_6 * (t_4 * ((b * b) - (a * a))))), 2.0))))) / ((double) M_PI));
	} else if (b <= 3.2e+157) {
		tmp = (180.0 / ((double) M_PI)) * atan((y_45_scale * (-0.5 * ((-2.0 / cos((((double) M_PI) * (angle * log(exp(0.005555555555555556)))))) * (t_1 / x_45_scale)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

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(pi * Float64(0.005555555555555556 * angle))
	t_1 = sin(t_0)
	t_2 = Float64(0.005555555555555556 * Float64(pi * angle))
	t_3 = Float64(atan(Float64(y_45_scale * Float64(-0.5 * Float64(2.0 / Float64(t_1 / Float64(cos(t_0) / x_45_scale)))))) * Float64(180.0 / pi))
	t_4 = sin(t_2)
	t_5 = cbrt(Float64(0.005555555555555556 * angle))
	t_6 = cos(t_2)
	t_7 = Float64(b * t_6) ^ 2.0
	tmp = 0.0
	if (b <= -1.05e+41)
		tmp = t_3;
	elseif (b <= 2.05e-100)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(Float64(y_45_scale / x_45_scale) * Float64(-2.0 * Float64(t_4 / cos(Float64((t_5 ^ 2.0) * Float64(pi * t_5)))))))) / pi));
	elseif (b <= 122000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(Float64(y_45_scale / x_45_scale) * sqrt((Float64(Float64(t_7 + fma(2.0, (Float64(t_4 * a) ^ 2.0), t_7)) / Float64(t_6 * Float64(t_4 * Float64(Float64(b * b) - Float64(a * a))))) ^ 2.0))))) / pi));
	elseif (b <= 3.2e+157)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(y_45_scale * Float64(-0.5 * Float64(Float64(-2.0 / cos(Float64(pi * Float64(angle * log(exp(0.005555555555555556)))))) * Float64(t_1 / x_45_scale))))));
	else
		tmp = t_3;
	end
	return tmp
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[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[ArcTan[N[(y$45$scale * N[(-0.5 * N[(2.0 / N[(t$95$1 / N[(N[Cos[t$95$0], $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Sin[t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[Power[N[(0.005555555555555556 * angle), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$6 = N[Cos[t$95$2], $MachinePrecision]}, Block[{t$95$7 = N[Power[N[(b * t$95$6), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[b, -1.05e+41], t$95$3, If[LessEqual[b, 2.05e-100], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[(y$45$scale / x$45$scale), $MachinePrecision] * N[(-2.0 * N[(t$95$4 / N[Cos[N[(N[Power[t$95$5, 2.0], $MachinePrecision] * N[(Pi * t$95$5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 122000.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[(y$45$scale / x$45$scale), $MachinePrecision] * N[Sqrt[N[Power[N[(N[(t$95$7 + N[(2.0 * N[Power[N[(t$95$4 * a), $MachinePrecision], 2.0], $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] / N[(t$95$6 * N[(t$95$4 * N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+157], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(y$45$scale * N[(-0.5 * N[(N[(-2.0 / N[Cos[N[(Pi * N[(angle * N[Log[N[Exp[0.005555555555555556], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(t$95$1 / x$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05e41 or 3.1999999999999999e157 < b

   1. Initial program 5.6%

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

   2. Simplified 3.7%

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

      [Start] 5.6

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

   3. Taylor expanded in y-scale around inf 9.1%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \color{blue}{\left(-0.5 \cdot \frac{x-scale \cdot \left(2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)}\right) \cdot \frac{180}{\pi} \]

   4. Simplified 6.8%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \color{blue}{\left(-0.5 \cdot \left(\frac{x-scale}{b \cdot b - a \cdot a} \cdot \frac{2 \cdot \left(\frac{b \cdot b}{x-scale \cdot x-scale} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \frac{a \cdot a}{x-scale \cdot x-scale} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)}\right) \cdot \frac{180}{\pi} \]
      Proof

      [Start] 9.1	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{x-scale \cdot \left(2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)\right) \cdot \frac{180}{\pi} \]
      times-frac [=>] 6.7	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(\frac{x-scale}{{b}^{2} - {a}^{2}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 6.7	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{x-scale}{\color{blue}{b \cdot b} - {a}^{2}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 6.7	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{x-scale}{b \cdot b - \color{blue}{a \cdot a}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]

   5. Taylor expanded in b around inf 59.2%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(2 \cdot \frac{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)\right) \cdot \frac{180}{\pi} \]

   6. Simplified 59.7%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\frac{2}{\frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{\frac{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}}}}\right)\right) \cdot \frac{180}{\pi} \]
      Proof

      [Start] 59.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(2 \cdot \frac{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r/ [=>] 59.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\frac{2 \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right) \cdot \frac{180}{\pi} \]
      associate-/l* [=>] 59.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\frac{2}{\frac{x-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}}\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 59.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot x-scale}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right) \cdot \frac{180}{\pi} \]
      associate-/l* [=>] 59.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\color{blue}{\frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\frac{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}}}}\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r* [=>] 59.4	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}{\frac{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}}}\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 59.4	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}{\frac{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}}}\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r* [=>] 59.7	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{\frac{\cos \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}{x-scale}}}\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 59.7	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{\frac{\cos \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}{x-scale}}}\right)\right) \cdot \frac{180}{\pi} \]

   if -1.05e41 < b < 2.0499999999999999e-100

   1. Initial program 15.9%

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

   2. Simplified 15.2%

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

      [Start] 15.9

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

   3. Taylor expanded in x-scale around 0 31.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{y-scale \cdot \left({b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)\right)}{x-scale \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right)}}{\pi} \]

   4. Simplified 34.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \frac{\mathsf{fma}\left(b \cdot b, {\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}, \mathsf{fma}\left(2, {\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2} \cdot \left(a \cdot a\right), \left(b \cdot b\right) \cdot {\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}\right)\right)}{\left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(b \cdot b - a \cdot a\right)}\right)\right)}}{\pi} \]
      Proof

      [Start] 31.5

      \[ 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{y-scale \cdot \left({b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)\right)}{x-scale \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right)}{\pi} \]

      times-frac [=>] 34.0

      \[ 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \color{blue}{\left(\frac{y-scale}{x-scale} \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)}\right)}{\pi} \]

   5. Taylor expanded in b around 0 58.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \color{blue}{\left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)\right)}{\pi} \]

   6. Applied egg-rr 58.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\cos \color{blue}{\left({\left(\sqrt[3]{\pi \cdot \left(0.005555555555555556 \cdot angle\right)}\right)}^{3}\right)}}\right)\right)\right)}{\pi} \]

   7. Applied egg-rr 58.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\cos \color{blue}{\left({\left(\sqrt[3]{0.005555555555555556 \cdot angle}\right)}^{2} \cdot \left(\sqrt[3]{0.005555555555555556 \cdot angle} \cdot \pi\right)\right)}}\right)\right)\right)}{\pi} \]

   if 2.0499999999999999e-100 < b < 122000

   1. Initial program 25.0%

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

   2. Simplified 23.3%

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

      [Start] 25.0

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

   3. Taylor expanded in x-scale around 0 43.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{y-scale \cdot \left({b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)\right)}{x-scale \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right)}}{\pi} \]

   4. Simplified 46.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \frac{\mathsf{fma}\left(b \cdot b, {\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}, \mathsf{fma}\left(2, {\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2} \cdot \left(a \cdot a\right), \left(b \cdot b\right) \cdot {\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}\right)\right)}{\left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(b \cdot b - a \cdot a\right)}\right)\right)}}{\pi} \]
      Proof

      [Start] 43.8

      \[ 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{y-scale \cdot \left({b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)\right)}{x-scale \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right)}{\pi} \]

      times-frac [=>] 46.2

      \[ 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \color{blue}{\left(\frac{y-scale}{x-scale} \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left(2 \cdot \left({a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right) + {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)}\right)}{\pi} \]

   5. Applied egg-rr 36.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \color{blue}{\sqrt{{\left(\frac{{\left(b \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + \mathsf{fma}\left(2, {\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot a\right)}^{2}, {\left(b \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}\right)}{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\right)}\right)}^{2}}}\right)\right)}{\pi} \]

   6. Simplified 36.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \color{blue}{\sqrt{{\left(\frac{{\left(b \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} + \mathsf{fma}\left(2, {\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2}, {\left(b \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2}\right)}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)}^{2}}}\right)\right)}{\pi} \]
      Proof

      [Start] 36.2

      \[ 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \sqrt{{\left(\frac{{\left(b \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} + \mathsf{fma}\left(2, {\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot a\right)}^{2}, {\left(b \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2}\right)}{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\right)}\right)}^{2}}\right)\right)}{\pi} \]

   if 122000 < b < 3.1999999999999999e157

   1. Initial program 22.7%

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

   2. Simplified 17.2%

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

      [Start] 22.7

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

   3. Taylor expanded in y-scale around inf 34.5%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \color{blue}{\left(-0.5 \cdot \frac{x-scale \cdot \left(2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)}\right) \cdot \frac{180}{\pi} \]

   4. Simplified 27.3%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \color{blue}{\left(-0.5 \cdot \left(\frac{x-scale}{b \cdot b - a \cdot a} \cdot \frac{2 \cdot \left(\frac{b \cdot b}{x-scale \cdot x-scale} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \frac{a \cdot a}{x-scale \cdot x-scale} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)}\right) \cdot \frac{180}{\pi} \]
      Proof

      [Start] 34.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{x-scale \cdot \left(2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}\right)}{\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right)\right) \cdot \frac{180}{\pi} \]
      times-frac [=>] 27.3	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(\frac{x-scale}{{b}^{2} - {a}^{2}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 27.3	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{x-scale}{\color{blue}{b \cdot b} - {a}^{2}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 27.3	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{x-scale}{b \cdot b - \color{blue}{a \cdot a}} \cdot \frac{2 \cdot \frac{{b}^{2} \cdot {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}} + 2 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{{x-scale}^{2}}}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]

   5. Taylor expanded in b around 0 39.5%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)\right) \cdot \frac{180}{\pi} \]

   6. Simplified 39.2%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(\frac{-2}{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)}\right)\right) \cdot \frac{180}{\pi} \]
      Proof

      [Start] 39.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r/ [=>] 39.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\frac{-2 \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 39.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{-2 \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{\color{blue}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot x-scale}}\right)\right) \cdot \frac{180}{\pi} \]
      times-frac [=>] 39.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \color{blue}{\left(\frac{-2}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)}\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r* [=>] 40.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}} \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 40.5	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}} \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      associate-*r* [=>] 39.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)} \cdot \frac{\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 39.2	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)} \cdot \frac{\sin \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]

   7. Applied egg-rr 20.4%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \color{blue}{\log \left({\left({\left(e^{0.005555555555555556}\right)}^{angle}\right)}^{\pi}\right)}} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]

   8. Simplified 39.3%

      \[\leadsto \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \color{blue}{\left(\pi \cdot \left(angle \cdot \log \left(e^{0.005555555555555556}\right)\right)\right)}} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      Proof

      [Start] 20.4	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \log \left({\left({\left(e^{0.005555555555555556}\right)}^{angle}\right)}^{\pi}\right)} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      log-pow [=>] 20.4	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \color{blue}{\left(\pi \cdot \log \left({\left(e^{0.005555555555555556}\right)}^{angle}\right)\right)}} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]
      log-pow [=>] 39.3	\[ \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \left(\pi \cdot \color{blue}{\left(angle \cdot \log \left(e^{0.005555555555555556}\right)\right)}\right)} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right) \cdot \frac{180}{\pi} \]

3. Recombined 4 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;\tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{\frac{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}}}\right)\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}{\cos \left({\left(\sqrt[3]{0.005555555555555556 \cdot angle}\right)}^{2} \cdot \left(\pi \cdot \sqrt[3]{0.005555555555555556 \cdot angle}\right)\right)}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;b \leq 122000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \sqrt{{\left(\frac{{\left(b \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2} + \mathsf{fma}\left(2, {\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot a\right)}^{2}, {\left(b \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\right)}{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\right)}\right)}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \left(\frac{-2}{\cos \left(\pi \cdot \left(angle \cdot \log \left(e^{0.005555555555555556}\right)\right)\right)} \cdot \frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{\frac{\cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}{x-scale}}}\right)\right) \cdot \frac{180}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	56.0%
Cost	59209

\[\begin{array}{l} t_0 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+43} \lor \neg \left(b \leq 2.9 \cdot 10^{+156}\right):\\ \;\;\;\;\tan^{-1} \left(y-scale \cdot \left(-0.5 \cdot \frac{2}{\frac{\sin t_0}{\frac{\cos t_0}{x-scale}}}\right)\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}{\cos \left(\sqrt{\pi} \cdot \left(\left(0.005555555555555556 \cdot angle\right) \cdot \sqrt{\pi}\right)\right)}\right)\right)\right)}{\pi}\\ \end{array} \]

Alternative 2
Accuracy	56.3%
Cost	53073

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ t_1 := \sin t_0\\ t_2 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan t_0 \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq -8400000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(2 \cdot \frac{\cos t_0}{t_1}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-148} \lor \neg \left(a \leq 6.5 \cdot 10^{-68}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(-2 \cdot \frac{t_1}{\cos \left({\left(\sqrt[3]{t_2}\right)}^{3}\right)}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \frac{2 \cdot \cos t_2}{\sin t_2}\right)\right)}{\pi}\\ \end{array} \]

Alternative 3
Accuracy	56.1%
Cost	46476

\[\begin{array}{l} t_0 := \sqrt[3]{\frac{y-scale}{x-scale}}\\ t_1 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \frac{2 \cdot \cos t_1}{\sin t_1}\right)\right)}{\pi}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left({t_0}^{2} \cdot \left(-2 \cdot \left(t_0 \cdot \tan t_1\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\left(y-scale \cdot \frac{-2}{x-scale}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)}{\pi}\\ \end{array} \]

Alternative 4
Accuracy	56.3%
Cost	40208

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ t_1 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(2 \cdot \frac{\cos t_0}{\sin t_0}\right)\right)\right)}{\pi}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan t_0 \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-2 \cdot \left(\frac{y-scale}{x-scale} \cdot \tan t_1\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\left(y-scale \cdot \frac{-2}{x-scale}\right) \cdot \sin t_1\right)\right)}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	56.3%
Cost	40208

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_1 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\frac{y-scale}{x-scale} \cdot \frac{2 \cdot \cos t_1}{\sin t_1}\right)\right)}{\pi}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-2 \cdot \left(\frac{y-scale}{x-scale} \cdot \tan t_0\right)\right)\right)}{\pi}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\left(y-scale \cdot \frac{-2}{x-scale}\right) \cdot \sin t_0\right)\right)}{\pi}\\ \end{array} \]

Alternative 6
Accuracy	46.2%
Cost	39820

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ t_1 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \frac{-2}{\pi \cdot x-scale}\right)\right)}{\pi}\\ t_3 := \sin t_1\\ \mathbf{if}\;angle \leq -1.46 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq -1.45 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;angle \leq 1.3 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{t_3}{\cos t_1 \cdot \frac{x-scale}{y-scale}}\right)\\ \mathbf{elif}\;angle \leq 8 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \left(\frac{x-scale}{\pi} \cdot \left(\frac{2}{b + a} \cdot \frac{\frac{a}{\frac{y-scale \cdot y-scale}{a}} - \frac{b}{x-scale} \cdot \frac{b}{x-scale}}{b - a}\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;angle \leq 2.1 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\left(y-scale \cdot \frac{-2}{x-scale}\right) \cdot t_3\right)\right)}{\pi}\\ \end{array} \]

Alternative 7
Accuracy	46.2%
Cost	27352

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \frac{-2}{\pi \cdot x-scale}\right)\right)}{\pi}\\ \mathbf{if}\;angle \leq -1.02 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq -1.05 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;angle \leq 2.9 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-0.011111111111111112 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \left(\frac{x-scale}{\pi} \cdot \left(\frac{2}{b + a} \cdot \frac{\frac{a}{\frac{y-scale \cdot y-scale}{a}} - \frac{b}{x-scale} \cdot \frac{b}{x-scale}}{b - a}\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;angle \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 2.6 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\left(y-scale \cdot \frac{-2}{x-scale}\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)}{\pi}\\ \end{array} \]

Alternative 8
Accuracy	53.1%
Cost	26824

\[\begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \frac{y-scale}{angle \cdot \left(\left(-0.5 \cdot \left(x-scale \cdot x-scale\right)\right) \cdot \frac{\pi}{x-scale}\right)}\right)}{\pi}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-2 \cdot \left(\frac{y-scale}{x-scale} \cdot \tan \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \frac{\frac{y-scale \cdot -2}{angle \cdot x-scale}}{\pi}\right)}{\pi}\\ \end{array} \]

Alternative 9
Accuracy	53.2%
Cost	26824

\[\begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \frac{y-scale}{angle \cdot \left(\left(-0.5 \cdot \left(x-scale \cdot x-scale\right)\right) \cdot \frac{\pi}{x-scale}\right)}\right)}{\pi}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(\tan \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\frac{y-scale}{x-scale} \cdot -2\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \frac{\frac{y-scale \cdot -2}{angle \cdot x-scale}}{\pi}\right)}{\pi}\\ \end{array} \]

Alternative 10
Accuracy	52.9%
Cost	20692

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(-2 \cdot \frac{y-scale}{x-scale \cdot \left(\pi \cdot angle\right)}\right)\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-0.011111111111111112 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)\right)\right)\right)}{\pi}\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{elif}\;b \leq 115000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Accuracy	52.9%
Cost	20692

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \frac{-2}{\pi \cdot x-scale}\right)\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-0.011111111111111112 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)\right)\right)\right)}{\pi}\\ \mathbf{if}\;b \leq -2.12 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -1050000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(-2 \cdot \frac{y-scale}{x-scale \cdot \left(\pi \cdot angle\right)}\right)\right)}{\pi}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{elif}\;b \leq 49000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Accuracy	52.8%
Cost	20684

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(90 \cdot \frac{y-scale}{angle \cdot \left(\left(-0.5 \cdot \left(x-scale \cdot x-scale\right)\right) \cdot \frac{\pi}{x-scale}\right)}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-0.011111111111111112 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)\right)\right)\right)}{\pi}\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -46000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 112000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(90 \cdot \left(\frac{y-scale}{angle} \cdot \frac{-2}{\pi \cdot x-scale}\right)\right)}{\pi}\\ \end{array} \]

Alternative 13
Accuracy	44.4%
Cost	20297

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-279} \lor \neg \left(a \leq 1.15 \cdot 10^{-180}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \left(-0.011111111111111112 \cdot \left(\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{x-scale}{y-scale \cdot \left(\pi \cdot angle\right)} \cdot -180\right)}}\\ \end{array} \]

Alternative 14
Accuracy	39.9%
Cost	20169

\[\begin{array}{l} \mathbf{if}\;b \leq 1.45 \cdot 10^{+192} \lor \neg \left(b \leq 6.6 \cdot 10^{+279}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-180 \cdot \frac{\frac{\frac{x-scale}{angle}}{\pi}}{y-scale}\right)}{\pi}\\ \end{array} \]

Alternative 15
Accuracy	40.0%
Cost	20168

\[\begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-180 \cdot \frac{x-scale}{y-scale \cdot angle}}{\pi}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \frac{y-scale \cdot \left(\pi \cdot angle\right)}{x-scale}\right)\\ \end{array} \]

Alternative 16
Accuracy	40.0%
Cost	20168

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-280}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-180 \cdot \frac{x-scale}{y-scale \cdot angle}}{\pi}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \frac{\pi \cdot \left(y-scale \cdot angle\right)}{x-scale}\right)\\ \end{array} \]

Alternative 17
Accuracy	40.0%
Cost	20168

\[\begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-280}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \left(\pi \cdot \frac{y-scale}{\frac{x-scale}{angle}}\right)\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-180}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{x-scale}{y-scale \cdot \left(\pi \cdot angle\right)} \cdot -180\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.005555555555555556 \cdot \frac{\pi \cdot \left(y-scale \cdot angle\right)}{x-scale}\right)\\ \end{array} \]

Alternative 18
Accuracy	13.3%
Cost	19904

\[180 \cdot \frac{\tan^{-1} \left(-180 \cdot \frac{\frac{\frac{x-scale}{angle}}{\pi}}{y-scale}\right)}{\pi} \]

Alternative 19
Accuracy	13.3%
Cost	19904

\[180 \cdot \frac{\tan^{-1} \left(\frac{-180}{\frac{y-scale}{x-scale} \cdot \left(\pi \cdot angle\right)}\right)}{\pi} \]

Reproduce

herbie shell --seed 2023125 
(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)))