ABCF->ab-angle angle

Average Error: 29.9 → 12.7

Time: 18.4s

Precision: binary64

Cost: 20164

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;A \leq -2800000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

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 (<= A -2800000.0)
   (/ (* 180.0 (atan (* 0.5 (+ (/ B A) (/ B (/ A (/ C A))))))) PI)
   (/ (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) 0.005555555555555556) PI)))

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 (A <= -2800000.0) {
		tmp = (180.0 * atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / ((double) M_PI);
	} else {
		tmp = (atan(((C - (A + hypot(B, (A - C)))) / B)) / 0.005555555555555556) / ((double) M_PI);
	}
	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 (A <= -2800000.0) {
		tmp = (180.0 * Math.atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / Math.PI;
	} else {
		tmp = (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / 0.005555555555555556) / Math.PI;
	}
	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 A <= -2800000.0:
		tmp = (180.0 * math.atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / math.pi
	else:
		tmp = (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / 0.005555555555555556) / math.pi
	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 (A <= -2800000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(B / Float64(A / Float64(C / A))))))) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / 0.005555555555555556) / pi);
	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 (A <= -2800000.0)
		tmp = (180.0 * atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / pi;
	else
		tmp = (atan(((C - (A + hypot(B, (A - C)))) / B)) / 0.005555555555555556) / pi;
	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[A, -2800000.0], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(B / N[(A / N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.8e6

   1. Initial program 48.4

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

   2. Simplified 48.4

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

      [Start] 48.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 48.4	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 48.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 48.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 48.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in A around -inf 23.4

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

   4. Simplified 21.8

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

      [Start] 23.4	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      distribute-lft-out [=>] 23.4	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C \cdot B}{{A}^{2}} + \frac{B}{A}\right)\right)}}{\pi} \]
      +-commutative [=>] 23.4	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(\frac{B}{A} + \frac{C \cdot B}{{A}^{2}}\right)}\right)}{\pi} \]
      *-commutative [=>] 23.4	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{\color{blue}{B \cdot C}}{{A}^{2}}\right)\right)}{\pi} \]
      associate-/l* [=>] 21.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \color{blue}{\frac{B}{\frac{{A}^{2}}{C}}}\right)\right)}{\pi} \]
      unpow2 [=>] 21.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{\color{blue}{A \cdot A}}{C}}\right)\right)}{\pi} \]
      associate-/l* [=>] 21.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\color{blue}{\frac{A}{\frac{C}{A}}}}\right)\right)}{\pi} \]

   if -2.8e6 < A

   1. Initial program 23.5

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

   2. Simplified 9.5

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

      [Start] 23.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 23.5	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 23.5	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 23.5	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 23.5	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 23.5	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 23.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 23.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 23.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 9.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   3. Applied egg-rr 9.5

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{0.005555555555555556}}{\pi}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 12.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2800000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	25.3
Cost	20364

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -2.25 \cdot 10^{-45}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -9 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)\\ \mathbf{elif}\;A \leq 4 \cdot 10^{-106} \lor \neg \left(A \leq 1.6 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.6
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -98000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)\\ \end{array} \]

Alternative 3
Error	12.7
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -40:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 4
Error	23.3
Cost	14353

\[\begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(B + C\right) - A\right) \cdot \frac{1}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-288} \lor \neg \left(B \leq 6.8 \cdot 10^{-101}\right) \land B \leq 4.9 \cdot 10^{-65}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	30.3
Cost	13973

\[\begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-173}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{2}{\frac{B}{C}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-59} \lor \neg \left(A \leq 1.3 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Error	33.0
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -5.3 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 8 \cdot 10^{-30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	33.0
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-308}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	32.9
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-309}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-2}{\frac{B}{A}}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	32.9
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{-192}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.42 \cdot 10^{-59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{2}{\frac{B}{C}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{-30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-2}{\frac{B}{A}}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	32.9
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.6 \cdot 10^{-305}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{2}{\frac{B}{C}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	25.0
Cost	13837

\[\begin{array}{l} \mathbf{if}\;A \leq -3.3 \cdot 10^{-28}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-59} \lor \neg \left(A \leq 1.3 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	24.8
Cost	13837

\[\begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-106} \lor \neg \left(A \leq 10^{-51}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	34.0
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -28000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Error	34.0
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 0.00019:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15
Error	38.3
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	50.5
Cost	13056

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

Reproduce

herbie shell --seed 2023016 
(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)))