ABCF->ab-angle angle

Average Accuracy: 54.0% → 81.1%

Time: 26.7s

Precision: binary64

Cost: 20164

Math

\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

↓

\[\begin{array}{l} \mathbf{if}\;C \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))

↓

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.5e+55)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (/ (atan (* (/ B C) -0.5)) (* PI 0.005555555555555556))))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}

↓

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.5e+55) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = atan(((B / C) * -0.5)) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
}

↓

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.5e+55) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = Math.atan(((B / C) * -0.5)) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)

↓

def code(A, B, C):
	tmp = 0
	if C <= 1.5e+55:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = math.atan(((B / C) * -0.5)) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end

↓

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.5e+55)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(B / C) * -0.5)) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
end

↓

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.5e+55)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = atan(((B / C) * -0.5)) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

↓

code[A_, B_, C_] := If[LessEqual[C, 1.5e+55], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.50000000000000008e55

   1. Initial program 64.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Simplified 86.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      Step-by-step derivation

      [Start] 64.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 64.3	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 64.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 64.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 64.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 64.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 86.7	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   if 1.50000000000000008e55 < C

   1. Initial program 18.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Simplified 41.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      Step-by-step derivation

      [Start] 18.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 18.5	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 18.5	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 18.5	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]
      *-lft-identity [=>] 18.5	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]
      sub-neg [=>] 18.5	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]
      associate-+l- [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]
      sub-neg [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]
      remove-double-neg [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]
      +-commutative [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]
      unpow2 [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]
      unpow2 [=>] 16.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]
      hypot-def [=>] 41.2	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Taylor expanded in C around inf 40.9%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B} + -1 \cdot \frac{A + -1 \cdot A}{B}\right)} \]

   4. Simplified 60.4%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{B \cdot C}, \frac{0}{B}\right)\right)} \]
      Step-by-step derivation

      [Start] 40.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B} + -1 \cdot \frac{A + -1 \cdot A}{B}\right) \]
      fma-def [=>] 40.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)} \]
      associate--l+ [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      unpow2 [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      fma-def [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      unpow2 [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      mul-1-neg [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - {\color{blue}{\left(-A\right)}}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      unpow2 [=>] 45.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-A\right) \cdot \left(-A\right)}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      difference-of-squares [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + \left(-A\right)\right) \cdot \left(A - \left(-A\right)\right)}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      mul-1-neg [<=] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(A + \color{blue}{-1 \cdot A}\right) \cdot \left(A - \left(-A\right)\right)\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      distribute-rgt1-in [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - \left(-A\right)\right)\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      metadata-eval [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - \left(-A\right)\right)\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      mul0-lft [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - \left(-A\right)\right)\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      *-commutative [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\color{blue}{B \cdot C}}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      associate-*r/ [=>] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{B \cdot C}, \color{blue}{\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}}\right)\right) \]

   5. Applied egg-rr 48.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \color{blue}{e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}}, \frac{0}{B}\right)\right) \]
      Step-by-step derivation

      [Start] 60.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{B \cdot C}, \frac{0}{B}\right)\right) \]
      add-exp-log [=>] 39.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \color{blue}{e^{\log \left(\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{B \cdot C}\right)}}, \frac{0}{B}\right)\right) \]
      add-sqr-sqrt [=>] 39.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\color{blue}{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}}{B \cdot C}\right)}, \frac{0}{B}\right)\right) \]
      *-commutative [=>] 39.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)} \cdot \sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{\color{blue}{C \cdot B}}\right)}, \frac{0}{B}\right)\right) \]
      times-frac [=>] 42.7	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \color{blue}{\left(\frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}}, \frac{0}{B}\right)\right) \]
      fma-udef [=>] 42.7	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\sqrt{\color{blue}{B \cdot B + 0 \cdot \left(A - \left(-A\right)\right)}}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}, \frac{0}{B}\right)\right) \]
      mul0-lft [=>] 42.7	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\sqrt{B \cdot B + \color{blue}{0}}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}, \frac{0}{B}\right)\right) \]
      +-rgt-identity [=>] 42.7	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\sqrt{\color{blue}{B \cdot B}}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}, \frac{0}{B}\right)\right) \]
      sqrt-unprod [<=] 31.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}, \frac{0}{B}\right)\right) \]
      add-sqr-sqrt [<=] 43.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{\color{blue}{B}}{C} \cdot \frac{\sqrt{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}}{B}\right)}, \frac{0}{B}\right)\right) \]
      fma-udef [=>] 43.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{\sqrt{\color{blue}{B \cdot B + 0 \cdot \left(A - \left(-A\right)\right)}}}{B}\right)}, \frac{0}{B}\right)\right) \]
      mul0-lft [=>] 43.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{\sqrt{B \cdot B + \color{blue}{0}}}{B}\right)}, \frac{0}{B}\right)\right) \]
      +-rgt-identity [=>] 43.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{\sqrt{\color{blue}{B \cdot B}}}{B}\right)}, \frac{0}{B}\right)\right) \]
      sqrt-unprod [<=] 38.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}{B}\right)}, \frac{0}{B}\right)\right) \]
      add-sqr-sqrt [<=] 48.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{\color{blue}{B}}{B}\right)}, \frac{0}{B}\right)\right) \]

   6. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}} \]
      Step-by-step derivation

      [Start] 48.1	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}, \frac{0}{B}\right)\right) \]
      clear-num [=>] 48.1	\[ \color{blue}{\frac{1}{\frac{\pi}{180}}} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}, \frac{0}{B}\right)\right) \]
      associate-*l/ [=>] 48.1	\[ \color{blue}{\frac{1 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}, \frac{0}{B}\right)\right)}{\frac{\pi}{180}}} \]
      *-un-lft-identity [<=] 48.1	\[ \frac{\color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}, \frac{0}{B}\right)\right)}}{\frac{\pi}{180}} \]
      fma-udef [=>] 48.1	\[ \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)} + \frac{0}{B}\right)}}{\frac{\pi}{180}} \]
      div0 [=>] 48.1	\[ \frac{\tan^{-1} \left(-0.5 \cdot e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)} + \color{blue}{0}\right)}{\frac{\pi}{180}} \]
      +-rgt-identity [=>] 48.1	\[ \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)}\right)}}{\frac{\pi}{180}} \]
      *-commutative [=>] 48.1	\[ \frac{\tan^{-1} \color{blue}{\left(e^{\log \left(\frac{B}{C} \cdot \frac{B}{B}\right)} \cdot -0.5\right)}}{\frac{\pi}{180}} \]
      add-exp-log [<=] 76.9	\[ \frac{\tan^{-1} \left(\color{blue}{\left(\frac{B}{C} \cdot \frac{B}{B}\right)} \cdot -0.5\right)}{\frac{\pi}{180}} \]
      *-inverses [=>] 76.9	\[ \frac{\tan^{-1} \left(\left(\frac{B}{C} \cdot \color{blue}{1}\right) \cdot -0.5\right)}{\frac{\pi}{180}} \]
      *-commutative [=>] 76.9	\[ \frac{\tan^{-1} \left(\color{blue}{\left(1 \cdot \frac{B}{C}\right)} \cdot -0.5\right)}{\frac{\pi}{180}} \]
      *-un-lft-identity [<=] 76.9	\[ \frac{\tan^{-1} \left(\color{blue}{\frac{B}{C}} \cdot -0.5\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 76.9	\[ \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	75.0%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+73}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot \left(0.5 \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \end{array} \]

Alternative 2
Accuracy	77.7%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;C \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right) \cdot -180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3
Accuracy	46.2%
Cost	14632

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -2.95 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -1.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{elif}\;C \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.65 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-145}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \end{array} \]

Alternative 4
Accuracy	46.3%
Cost	14632

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -2.1 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.9 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -4.7 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -3.6 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	46.2%
Cost	14632

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -5.7 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -5.3 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.06 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -8.2 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]

Alternative 6
Accuracy	46.4%
Cost	14632

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -6.9 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -5.6 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -2.7 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.85 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.15 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]

Alternative 7
Accuracy	60.7%
Cost	14496

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{if}\;B \leq 8.6 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 155:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Accuracy	53.9%
Cost	14104

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;C \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -6.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;C \leq -2.8 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.85 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -7.2 \cdot 10^{-234}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]

Alternative 9
Accuracy	53.7%
Cost	14104

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;C \leq -7.5 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -4.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;C \leq -2.8 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -5.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 8.4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 10
Accuracy	65.9%
Cost	14088

\[\begin{array}{l} \mathbf{if}\;B \leq 1.02 \cdot 10^{-171}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-129}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 11
Accuracy	58.9%
Cost	14036

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-239}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \]

Alternative 12
Accuracy	56.0%
Cost	13972

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 235000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \]

Alternative 13
Accuracy	65.3%
Cost	13969

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{if}\;B \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-98} \lor \neg \left(B \leq 1.9 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \end{array} \]

Alternative 14
Accuracy	65.9%
Cost	13960

\[\begin{array}{l} \mathbf{if}\;B \leq 1.05 \cdot 10^{-171}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot \left(0.5 \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 15
Accuracy	56.5%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;C \leq -1.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{2}{\frac{B}{C}}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -8.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 9 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 16
Accuracy	59.3%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;C \leq -2.25 \cdot 10^{-112}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -8.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 17
Accuracy	46.0%
Cost	13712

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4 \cdot 10^{-102}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.02 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Accuracy	46.1%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Accuracy	39.5%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20
Accuracy	20.9%
Cost	13056

\[\frac{180 \cdot \tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023157 
(FPCore (A B C)
  :name "ABCF->ab-angle angle"
  :precision binary64
  (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))) PI)))