raw-angle from scale-rotated-ellipse

Average Error: 55.1 → 34.9

Time: 2.2min

Precision: binary64

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 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := y-scale \cdot {x-scale}^{-2}\\ t_2 := \sin t_0\\ t_3 := t_2 \cdot t_1\\ t_4 := 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{{\cos t_0}^{2}}{x-scale \cdot x-scale} \cdot \frac{-y-scale}{t_2}\right)\right)}{\pi}\\ t_5 := \frac{y-scale}{x-scale \cdot x-scale}\\ t_6 := 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(t_5 \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right)}{\pi}\\ t_7 := 180 \cdot \frac{\tan^{-1} \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot \frac{y-scale}{x-scale}\right)\right)}{\pi}\\ t_8 := 180 \cdot \frac{\tan^{-1} \left(\frac{y-scale \cdot t_2}{x-scale}\right)}{\pi}\\ \mathbf{if}\;x-scale \leq -3.2116766629260986 \cdot 10^{+154}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x-scale \leq -9.84452925613738 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x-scale \leq -1.242420305716196 \cdot 10^{-42}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x-scale \leq -5.6248734637854445 \cdot 10^{-99}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x-scale \leq -4.8060553385269945 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\frac{y-scale}{x-scale} \cdot t_2}{x-scale}\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -6.253184033580119 \cdot 10^{-243}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \sqrt{{t_3}^{2}}\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 1.6582340324706763 \cdot 10^{-307}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x-scale \leq 5.147224452517122 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(t_2 \cdot {\left({t_1}^{3}\right)}^{0.3333333333333333}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 8.191269321848878 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(t_0 \cdot t_5\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 1.4303173329051239 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(t_5 \cdot \left(t_0 + \left({angle}^{3} \cdot {\pi}^{3}\right) \cdot -2.8577960676726107 \cdot 10^{-8}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 8.962533660054582 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(t_3\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 2.8859830434113404 \cdot 10^{-37}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x-scale \leq 1.8322237614678637 \cdot 10^{+34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x-scale \leq 7.22517356074486 \cdot 10^{+120}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \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 (* 0.005555555555555556 (* angle PI)))
        (t_1 (* y-scale (pow x-scale -2.0)))
        (t_2 (sin t_0))
        (t_3 (* t_2 t_1))
        (t_4
         (*
          180.0
          (/
           (atan
            (*
             x-scale
             (*
              (/ (pow (cos t_0) 2.0) (* x-scale x-scale))
              (/ (- y-scale) t_2))))
           PI)))
        (t_5 (/ y-scale (* x-scale x-scale)))
        (t_6
         (*
          180.0
          (/
           (atan
            (*
             x-scale
             (*
              t_5
              (expm1 (log1p (sin (* angle (* 0.005555555555555556 PI))))))))
           PI)))
        (t_7
         (*
          180.0
          (/
           (atan (* 0.005555555555555556 (* (* angle PI) (/ y-scale x-scale))))
           PI)))
        (t_8 (* 180.0 (/ (atan (/ (* y-scale t_2) x-scale)) PI))))
   (if (<= x-scale -3.2116766629260986e+154)
     t_7
     (if (<= x-scale -9.84452925613738e+111)
       t_4
       (if (<= x-scale -1.242420305716196e-42)
         t_8
         (if (<= x-scale -5.6248734637854445e-99)
           t_4
           (if (<= x-scale -4.8060553385269945e-197)
             (*
              180.0
              (/
               (atan (* x-scale (/ (* (/ y-scale x-scale) t_2) x-scale)))
               PI))
             (if (<= x-scale -6.253184033580119e-243)
               (* 180.0 (/ (atan (* x-scale (sqrt (pow t_3 2.0)))) PI))
               (if (<= x-scale 1.6582340324706763e-307)
                 t_6
                 (if (<= x-scale 5.147224452517122e-270)
                   (*
                    180.0
                    (/
                     (atan
                      (*
                       x-scale
                       (* t_2 (pow (pow t_1 3.0) 0.3333333333333333))))
                     PI))
                   (if (<= x-scale 8.191269321848878e-218)
                     (* 180.0 (/ (atan (* x-scale (* t_0 t_5))) PI))
                     (if (<= x-scale 1.4303173329051239e-126)
                       (*
                        180.0
                        (/
                         (atan
                          (*
                           x-scale
                           (*
                            t_5
                            (+
                             t_0
                             (*
                              (* (pow angle 3.0) (pow PI 3.0))
                              -2.8577960676726107e-8)))))
                         PI))
                       (if (<= x-scale 8.962533660054582e-101)
                         (*
                          180.0
                          (/ (atan (* x-scale (log1p (expm1 t_3)))) PI))
                         (if (<= x-scale 2.8859830434113404e-37)
                           t_6
                           (if (<= x-scale 1.8322237614678637e+34)
                             t_4
                             (if (<= x-scale 7.22517356074486e+120)
                               t_7
                               t_8))))))))))))))))

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 = 0.005555555555555556 * (angle * ((double) M_PI));
	double t_1 = y_45_scale * pow(x_45_scale, -2.0);
	double t_2 = sin(t_0);
	double t_3 = t_2 * t_1;
	double t_4 = 180.0 * (atan((x_45_scale * ((pow(cos(t_0), 2.0) / (x_45_scale * x_45_scale)) * (-y_45_scale / t_2)))) / ((double) M_PI));
	double t_5 = y_45_scale / (x_45_scale * x_45_scale);
	double t_6 = 180.0 * (atan((x_45_scale * (t_5 * expm1(log1p(sin((angle * (0.005555555555555556 * ((double) M_PI))))))))) / ((double) M_PI));
	double t_7 = 180.0 * (atan((0.005555555555555556 * ((angle * ((double) M_PI)) * (y_45_scale / x_45_scale)))) / ((double) M_PI));
	double t_8 = 180.0 * (atan(((y_45_scale * t_2) / x_45_scale)) / ((double) M_PI));
	double tmp;
	if (x_45_scale <= -3.2116766629260986e+154) {
		tmp = t_7;
	} else if (x_45_scale <= -9.84452925613738e+111) {
		tmp = t_4;
	} else if (x_45_scale <= -1.242420305716196e-42) {
		tmp = t_8;
	} else if (x_45_scale <= -5.6248734637854445e-99) {
		tmp = t_4;
	} else if (x_45_scale <= -4.8060553385269945e-197) {
		tmp = 180.0 * (atan((x_45_scale * (((y_45_scale / x_45_scale) * t_2) / x_45_scale))) / ((double) M_PI));
	} else if (x_45_scale <= -6.253184033580119e-243) {
		tmp = 180.0 * (atan((x_45_scale * sqrt(pow(t_3, 2.0)))) / ((double) M_PI));
	} else if (x_45_scale <= 1.6582340324706763e-307) {
		tmp = t_6;
	} else if (x_45_scale <= 5.147224452517122e-270) {
		tmp = 180.0 * (atan((x_45_scale * (t_2 * pow(pow(t_1, 3.0), 0.3333333333333333)))) / ((double) M_PI));
	} else if (x_45_scale <= 8.191269321848878e-218) {
		tmp = 180.0 * (atan((x_45_scale * (t_0 * t_5))) / ((double) M_PI));
	} else if (x_45_scale <= 1.4303173329051239e-126) {
		tmp = 180.0 * (atan((x_45_scale * (t_5 * (t_0 + ((pow(angle, 3.0) * pow(((double) M_PI), 3.0)) * -2.8577960676726107e-8))))) / ((double) M_PI));
	} else if (x_45_scale <= 8.962533660054582e-101) {
		tmp = 180.0 * (atan((x_45_scale * log1p(expm1(t_3)))) / ((double) M_PI));
	} else if (x_45_scale <= 2.8859830434113404e-37) {
		tmp = t_6;
	} else if (x_45_scale <= 1.8322237614678637e+34) {
		tmp = t_4;
	} else if (x_45_scale <= 7.22517356074486e+120) {
		tmp = t_7;
	} else {
		tmp = t_8;
	}
	return tmp;
}

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 = 0.005555555555555556 * (angle * Math.PI);
	double t_1 = y_45_scale * Math.pow(x_45_scale, -2.0);
	double t_2 = Math.sin(t_0);
	double t_3 = t_2 * t_1;
	double t_4 = 180.0 * (Math.atan((x_45_scale * ((Math.pow(Math.cos(t_0), 2.0) / (x_45_scale * x_45_scale)) * (-y_45_scale / t_2)))) / Math.PI);
	double t_5 = y_45_scale / (x_45_scale * x_45_scale);
	double t_6 = 180.0 * (Math.atan((x_45_scale * (t_5 * Math.expm1(Math.log1p(Math.sin((angle * (0.005555555555555556 * Math.PI)))))))) / Math.PI);
	double t_7 = 180.0 * (Math.atan((0.005555555555555556 * ((angle * Math.PI) * (y_45_scale / x_45_scale)))) / Math.PI);
	double t_8 = 180.0 * (Math.atan(((y_45_scale * t_2) / x_45_scale)) / Math.PI);
	double tmp;
	if (x_45_scale <= -3.2116766629260986e+154) {
		tmp = t_7;
	} else if (x_45_scale <= -9.84452925613738e+111) {
		tmp = t_4;
	} else if (x_45_scale <= -1.242420305716196e-42) {
		tmp = t_8;
	} else if (x_45_scale <= -5.6248734637854445e-99) {
		tmp = t_4;
	} else if (x_45_scale <= -4.8060553385269945e-197) {
		tmp = 180.0 * (Math.atan((x_45_scale * (((y_45_scale / x_45_scale) * t_2) / x_45_scale))) / Math.PI);
	} else if (x_45_scale <= -6.253184033580119e-243) {
		tmp = 180.0 * (Math.atan((x_45_scale * Math.sqrt(Math.pow(t_3, 2.0)))) / Math.PI);
	} else if (x_45_scale <= 1.6582340324706763e-307) {
		tmp = t_6;
	} else if (x_45_scale <= 5.147224452517122e-270) {
		tmp = 180.0 * (Math.atan((x_45_scale * (t_2 * Math.pow(Math.pow(t_1, 3.0), 0.3333333333333333)))) / Math.PI);
	} else if (x_45_scale <= 8.191269321848878e-218) {
		tmp = 180.0 * (Math.atan((x_45_scale * (t_0 * t_5))) / Math.PI);
	} else if (x_45_scale <= 1.4303173329051239e-126) {
		tmp = 180.0 * (Math.atan((x_45_scale * (t_5 * (t_0 + ((Math.pow(angle, 3.0) * Math.pow(Math.PI, 3.0)) * -2.8577960676726107e-8))))) / Math.PI);
	} else if (x_45_scale <= 8.962533660054582e-101) {
		tmp = 180.0 * (Math.atan((x_45_scale * Math.log1p(Math.expm1(t_3)))) / Math.PI);
	} else if (x_45_scale <= 2.8859830434113404e-37) {
		tmp = t_6;
	} else if (x_45_scale <= 1.8322237614678637e+34) {
		tmp = t_4;
	} else if (x_45_scale <= 7.22517356074486e+120) {
		tmp = t_7;
	} else {
		tmp = t_8;
	}
	return tmp;
}

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 = 0.005555555555555556 * (angle * math.pi)
	t_1 = y_45_scale * math.pow(x_45_scale, -2.0)
	t_2 = math.sin(t_0)
	t_3 = t_2 * t_1
	t_4 = 180.0 * (math.atan((x_45_scale * ((math.pow(math.cos(t_0), 2.0) / (x_45_scale * x_45_scale)) * (-y_45_scale / t_2)))) / math.pi)
	t_5 = y_45_scale / (x_45_scale * x_45_scale)
	t_6 = 180.0 * (math.atan((x_45_scale * (t_5 * math.expm1(math.log1p(math.sin((angle * (0.005555555555555556 * math.pi)))))))) / math.pi)
	t_7 = 180.0 * (math.atan((0.005555555555555556 * ((angle * math.pi) * (y_45_scale / x_45_scale)))) / math.pi)
	t_8 = 180.0 * (math.atan(((y_45_scale * t_2) / x_45_scale)) / math.pi)
	tmp = 0
	if x_45_scale <= -3.2116766629260986e+154:
		tmp = t_7
	elif x_45_scale <= -9.84452925613738e+111:
		tmp = t_4
	elif x_45_scale <= -1.242420305716196e-42:
		tmp = t_8
	elif x_45_scale <= -5.6248734637854445e-99:
		tmp = t_4
	elif x_45_scale <= -4.8060553385269945e-197:
		tmp = 180.0 * (math.atan((x_45_scale * (((y_45_scale / x_45_scale) * t_2) / x_45_scale))) / math.pi)
	elif x_45_scale <= -6.253184033580119e-243:
		tmp = 180.0 * (math.atan((x_45_scale * math.sqrt(math.pow(t_3, 2.0)))) / math.pi)
	elif x_45_scale <= 1.6582340324706763e-307:
		tmp = t_6
	elif x_45_scale <= 5.147224452517122e-270:
		tmp = 180.0 * (math.atan((x_45_scale * (t_2 * math.pow(math.pow(t_1, 3.0), 0.3333333333333333)))) / math.pi)
	elif x_45_scale <= 8.191269321848878e-218:
		tmp = 180.0 * (math.atan((x_45_scale * (t_0 * t_5))) / math.pi)
	elif x_45_scale <= 1.4303173329051239e-126:
		tmp = 180.0 * (math.atan((x_45_scale * (t_5 * (t_0 + ((math.pow(angle, 3.0) * math.pow(math.pi, 3.0)) * -2.8577960676726107e-8))))) / math.pi)
	elif x_45_scale <= 8.962533660054582e-101:
		tmp = 180.0 * (math.atan((x_45_scale * math.log1p(math.expm1(t_3)))) / math.pi)
	elif x_45_scale <= 2.8859830434113404e-37:
		tmp = t_6
	elif x_45_scale <= 1.8322237614678637e+34:
		tmp = t_4
	elif x_45_scale <= 7.22517356074486e+120:
		tmp = t_7
	else:
		tmp = t_8
	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(0.005555555555555556 * Float64(angle * pi))
	t_1 = Float64(y_45_scale * (x_45_scale ^ -2.0))
	t_2 = sin(t_0)
	t_3 = Float64(t_2 * t_1)
	t_4 = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(Float64((cos(t_0) ^ 2.0) / Float64(x_45_scale * x_45_scale)) * Float64(Float64(-y_45_scale) / t_2)))) / pi))
	t_5 = Float64(y_45_scale / Float64(x_45_scale * x_45_scale))
	t_6 = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(t_5 * expm1(log1p(sin(Float64(angle * Float64(0.005555555555555556 * pi)))))))) / pi))
	t_7 = Float64(180.0 * Float64(atan(Float64(0.005555555555555556 * Float64(Float64(angle * pi) * Float64(y_45_scale / x_45_scale)))) / pi))
	t_8 = Float64(180.0 * Float64(atan(Float64(Float64(y_45_scale * t_2) / x_45_scale)) / pi))
	tmp = 0.0
	if (x_45_scale <= -3.2116766629260986e+154)
		tmp = t_7;
	elseif (x_45_scale <= -9.84452925613738e+111)
		tmp = t_4;
	elseif (x_45_scale <= -1.242420305716196e-42)
		tmp = t_8;
	elseif (x_45_scale <= -5.6248734637854445e-99)
		tmp = t_4;
	elseif (x_45_scale <= -4.8060553385269945e-197)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(Float64(Float64(y_45_scale / x_45_scale) * t_2) / x_45_scale))) / pi));
	elseif (x_45_scale <= -6.253184033580119e-243)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * sqrt((t_3 ^ 2.0)))) / pi));
	elseif (x_45_scale <= 1.6582340324706763e-307)
		tmp = t_6;
	elseif (x_45_scale <= 5.147224452517122e-270)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(t_2 * ((t_1 ^ 3.0) ^ 0.3333333333333333)))) / pi));
	elseif (x_45_scale <= 8.191269321848878e-218)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(t_0 * t_5))) / pi));
	elseif (x_45_scale <= 1.4303173329051239e-126)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * Float64(t_5 * Float64(t_0 + Float64(Float64((angle ^ 3.0) * (pi ^ 3.0)) * -2.8577960676726107e-8))))) / pi));
	elseif (x_45_scale <= 8.962533660054582e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(x_45_scale * log1p(expm1(t_3)))) / pi));
	elseif (x_45_scale <= 2.8859830434113404e-37)
		tmp = t_6;
	elseif (x_45_scale <= 1.8322237614678637e+34)
		tmp = t_4;
	elseif (x_45_scale <= 7.22517356074486e+120)
		tmp = t_7;
	else
		tmp = t_8;
	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[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y$45$scale * N[Power[x$45$scale, -2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(N[(N[Power[N[Cos[t$95$0], $MachinePrecision], 2.0], $MachinePrecision] / N[(x$45$scale * x$45$scale), $MachinePrecision]), $MachinePrecision] * N[((-y$45$scale) / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y$45$scale / N[(x$45$scale * x$45$scale), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(t$95$5 * N[(Exp[N[Log[1 + N[Sin[N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(180.0 * N[(N[ArcTan[N[(0.005555555555555556 * N[(N[(angle * Pi), $MachinePrecision] * N[(y$45$scale / x$45$scale), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(180.0 * N[(N[ArcTan[N[(N[(y$45$scale * t$95$2), $MachinePrecision] / x$45$scale), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$45$scale, -3.2116766629260986e+154], t$95$7, If[LessEqual[x$45$scale, -9.84452925613738e+111], t$95$4, If[LessEqual[x$45$scale, -1.242420305716196e-42], t$95$8, If[LessEqual[x$45$scale, -5.6248734637854445e-99], t$95$4, If[LessEqual[x$45$scale, -4.8060553385269945e-197], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(N[(N[(y$45$scale / x$45$scale), $MachinePrecision] * t$95$2), $MachinePrecision] / x$45$scale), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, -6.253184033580119e-243], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[Sqrt[N[Power[t$95$3, 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 1.6582340324706763e-307], t$95$6, If[LessEqual[x$45$scale, 5.147224452517122e-270], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(t$95$2 * N[Power[N[Power[t$95$1, 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 8.191269321848878e-218], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(t$95$0 * t$95$5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 1.4303173329051239e-126], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[(t$95$5 * N[(t$95$0 + N[(N[(N[Power[angle, 3.0], $MachinePrecision] * N[Power[Pi, 3.0], $MachinePrecision]), $MachinePrecision] * -2.8577960676726107e-8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 8.962533660054582e-101], N[(180.0 * N[(N[ArcTan[N[(x$45$scale * N[Log[1 + N[(Exp[t$95$3] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$45$scale, 2.8859830434113404e-37], t$95$6, If[LessEqual[x$45$scale, 1.8322237614678637e+34], t$95$4, If[LessEqual[x$45$scale, 7.22517356074486e+120], t$95$7, t$95$8]]]]]]]]]]]]]]]]]]]]]]]

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Bits error versus x-scale

Bits error versus y-scale

Derivation

1. Split input into 10 regimes

2. if x-scale < -3.21167666292609857e154 or 1.8322237614678637e34 < x-scale < 7.2251735607448595e120

   1. Initial program 59.9

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

   2. Simplified 58.3

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

   3. Taylor expanded in x-scale around 0 54.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 54.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 54.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 37.0

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

   7. Simplified 37.0

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

   8. Taylor expanded in angle around 0 36.9

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

   9. Simplified 32.1

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

   if -3.21167666292609857e154 < x-scale < -9.84452925613738043e111 or -1.242420305716196e-42 < x-scale < -5.6248734637854445e-99 or 2.8859830434113404e-37 < x-scale < 1.8322237614678637e34

   1. Initial program 52.1

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

   2. Simplified 51.3

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

   3. Taylor expanded in x-scale around 0 49.8

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 49.8

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 50.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around 0 38.8

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

   7. Simplified 38.7

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

   if -9.84452925613738043e111 < x-scale < -1.242420305716196e-42 or 7.2251735607448595e120 < x-scale

   1. Initial program 58.6

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

   2. Simplified 57.4

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

   3. Taylor expanded in x-scale around 0 54.4

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 54.4

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 54.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 37.2

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

   7. Simplified 37.1

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

   8. Taylor expanded in x-scale around 0 32.5

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

   if -5.6248734637854445e-99 < x-scale < -4.8060553385269945e-197

   1. Initial program 51.2

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

   2. Simplified 48.7

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

   3. Taylor expanded in x-scale around 0 47.8

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 47.8

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 47.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 38.2

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

   7. Simplified 36.5

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

   8. Applied egg-rr 34.6

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

   if -4.8060553385269945e-197 < x-scale < -6.25318403358011933e-243

   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 51.6

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

   3. Taylor expanded in x-scale around 0 51.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 51.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 50.6

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 38.3

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

   7. Simplified 38.1

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

   8. Applied egg-rr 36.4

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

   if -6.25318403358011933e-243 < x-scale < 1.6582340324706763e-307 or 8.96253366005458249e-101 < x-scale < 2.8859830434113404e-37

   1. Initial program 51.4

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

   2. Simplified 48.6

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

   3. Taylor expanded in x-scale around 0 47.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 47.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 47.6

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 38.6

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

   7. Simplified 37.1

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

   8. Applied egg-rr 37.2

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{y-scale}{x-scale \cdot x-scale} \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)}\right)\right)}{\pi} \]

   if 1.6582340324706763e-307 < x-scale < 5.1472244525171218e-270

   1. Initial program 53.4

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

   2. Simplified 47.8

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

   3. Taylor expanded in x-scale around 0 44.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 44.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 46.2

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 36.9

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

   7. Simplified 35.1

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

   8. Applied egg-rr 32.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\color{blue}{{\left({\left(y-scale \cdot {x-scale}^{-2}\right)}^{3}\right)}^{0.3333333333333333}} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}{\pi} \]

   if 5.1472244525171218e-270 < x-scale < 8.19126932184887821e-218

   1. Initial program 50.7

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

   2. Simplified 46.6

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

   3. Taylor expanded in x-scale around 0 44.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 44.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 44.2

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 39.8

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

   7. Simplified 39.2

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

   8. Taylor expanded in angle around 0 37.9

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

   if 8.19126932184887821e-218 < x-scale < 1.4303173329051239e-126

   1. Initial program 49.8

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

   2. Simplified 47.6

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

   3. Taylor expanded in x-scale around 0 46.2

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 46.2

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 46.4

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 41.3

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

   7. Simplified 39.7

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

   8. Taylor expanded in angle around 0 38.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{y-scale}{x-scale \cdot x-scale} \cdot \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right) - 2.8577960676726107 \cdot 10^{-8} \cdot \left({angle}^{3} \cdot {\pi}^{3}\right)\right)}\right)\right)}{\pi} \]

   if 1.4303173329051239e-126 < x-scale < 8.96253366005458249e-101

   1. Initial program 49.2

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

   2. Simplified 48.4

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

   3. Taylor expanded in x-scale around 0 48.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{{a}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot {b}^{2} + \sqrt{2 \cdot \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right)\right) + \left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4} \cdot {b}^{4} + {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)}\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   4. Simplified 48.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\color{blue}{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\cos \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   5. Taylor expanded in angle around 0 48.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left({a}^{2}, {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}, {b}^{2}, \sqrt{\mathsf{fma}\left(2, {\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}\right)\right), \mathsf{fma}\left({\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}, {b}^{4}, {a}^{4} \cdot {\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{4}\right)\right)}\right)\right)}{{x-scale}^{2}}}{\frac{\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\color{blue}{1} \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}{y-scale}}\right)}{\pi} \]

   6. Taylor expanded in a around inf 39.5

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

   7. Simplified 36.8

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

   8. Applied egg-rr 38.4

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\left(y-scale \cdot {x-scale}^{-2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}\right)}{\pi} \]
3. Recombined 10 regimes into one program.

4. Final simplification 34.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x-scale \leq -3.2116766629260986 \cdot 10^{+154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot \frac{y-scale}{x-scale}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -9.84452925613738 \cdot 10^{+111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{-y-scale}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -1.242420305716196 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{y-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -5.6248734637854445 \cdot 10^{-99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{-y-scale}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -4.8060553385269945 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \frac{\frac{y-scale}{x-scale} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq -6.253184033580119 \cdot 10^{-243}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \sqrt{{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(y-scale \cdot {x-scale}^{-2}\right)\right)}^{2}}\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 1.6582340324706763 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{y-scale}{x-scale \cdot x-scale} \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 5.147224452517122 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot {\left({\left(y-scale \cdot {x-scale}^{-2}\right)}^{3}\right)}^{0.3333333333333333}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 8.191269321848878 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \frac{y-scale}{x-scale \cdot x-scale}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 1.4303173329051239 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{y-scale}{x-scale \cdot x-scale} \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right) + \left({angle}^{3} \cdot {\pi}^{3}\right) \cdot -2.8577960676726107 \cdot 10^{-8}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 8.962533660054582 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(y-scale \cdot {x-scale}^{-2}\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 2.8859830434113404 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{y-scale}{x-scale \cdot x-scale} \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 1.8322237614678637 \cdot 10^{+34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(x-scale \cdot \left(\frac{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{2}}{x-scale \cdot x-scale} \cdot \frac{-y-scale}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)}{\pi}\\ \mathbf{elif}\;x-scale \leq 7.22517356074486 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.005555555555555556 \cdot \left(\left(angle \cdot \pi\right) \cdot \frac{y-scale}{x-scale}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{y-scale \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{x-scale}\right)}{\pi}\\ \end{array} \]

Reproduce

herbie shell --seed 2022151 
(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)))