ABCF->ab-angle angle

Average Error: 46.07% → 18.75%

Time: 19.0s

Precision: binary64

Cost: 20164

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

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 -1.5e+85)
   (/ (* 180.0 (atan (* 0.5 (* (/ B A) (+ 1.0 (/ C A)))))) PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) 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 <= -1.5e+85) {
		tmp = (180.0 * atan((0.5 * ((B / A) * (1.0 + (C / A)))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((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 <= -1.5e+85) {
		tmp = (180.0 * Math.atan((0.5 * ((B / A) * (1.0 + (C / A)))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / 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 <= -1.5e+85:
		tmp = (180.0 * math.atan((0.5 * ((B / A) * (1.0 + (C / A)))))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / 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 <= -1.5e+85)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(Float64(B / A) * Float64(1.0 + Float64(C / A)))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / 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 <= -1.5e+85)
		tmp = (180.0 * atan((0.5 * ((B / A) * (1.0 + (C / A)))))) / pi;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / 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, -1.5e+85], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] * N[(1.0 + N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if A < -1.5e85

   1. Initial program 82.06

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

   2. Simplified 82.06

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

      [Start] 82.06	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 82.06	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 82.06	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 82.06	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 82.06	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in A around -inf 30.48

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

   4. Simplified 26.08

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

      [Start] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      distribute-lft-out [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C \cdot B}{{A}^{2}} + \frac{B}{A}\right)\right)}}{\pi} \]
      +-commutative [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(\frac{B}{A} + \frac{C \cdot B}{{A}^{2}}\right)}\right)}{\pi} \]
      *-commutative [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{\color{blue}{B \cdot C}}{{A}^{2}}\right)\right)}{\pi} \]
      associate-/l* [=>] 25.78	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \color{blue}{\frac{B}{\frac{{A}^{2}}{C}}}\right)\right)}{\pi} \]
      unpow2 [=>] 25.78	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{\color{blue}{A \cdot A}}{C}}\right)\right)}{\pi} \]
      associate-/l* [=>] 26.08	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\color{blue}{\frac{A}{\frac{C}{A}}}}\right)\right)}{\pi} \]

   5. Taylor expanded in B around 0 25.82

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

   6. Simplified 25.23

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

      [Start] 25.82	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\left(\frac{C}{{A}^{2}} + \frac{1}{A}\right) \cdot B\right)\right)}{\pi} \]
      *-commutative [=>] 25.82	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(B \cdot \left(\frac{C}{{A}^{2}} + \frac{1}{A}\right)\right)}\right)}{\pi} \]
      +-commutative [=>] 25.82	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \color{blue}{\left(\frac{1}{A} + \frac{C}{{A}^{2}}\right)}\right)\right)}{\pi} \]
      unpow2 [=>] 25.82	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{C}{\color{blue}{A \cdot A}}\right)\right)\right)}{\pi} \]
      distribute-lft-in [=>] 25.82	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(B \cdot \frac{1}{A} + B \cdot \frac{C}{A \cdot A}\right)}\right)}{\pi} \]
      associate-*r/ [=>] 30.52	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{1}{A} + \color{blue}{\frac{B \cdot C}{A \cdot A}}\right)\right)}{\pi} \]
      *-commutative [<=] 30.52	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{1}{A} + \frac{\color{blue}{C \cdot B}}{A \cdot A}\right)\right)}{\pi} \]
      unpow2 [<=] 30.52	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{1}{A} + \frac{C \cdot B}{\color{blue}{{A}^{2}}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\color{blue}{\frac{B \cdot 1}{A}} + \frac{C \cdot B}{{A}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [<=] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\color{blue}{\frac{B}{A} \cdot 1} + \frac{C \cdot B}{{A}^{2}}\right)\right)}{\pi} \]
      *-commutative [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\color{blue}{1 \cdot \frac{B}{A}} + \frac{C \cdot B}{{A}^{2}}\right)\right)}{\pi} \]
      unpow2 [=>] 30.48	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(1 \cdot \frac{B}{A} + \frac{C \cdot B}{\color{blue}{A \cdot A}}\right)\right)}{\pi} \]
      times-frac [=>] 25.23	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(1 \cdot \frac{B}{A} + \color{blue}{\frac{C}{A} \cdot \frac{B}{A}}\right)\right)}{\pi} \]
      distribute-rgt-out [=>] 25.23	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)}\right)}{\pi} \]

   if -1.5e85 < A

   1. Initial program 38.84

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

   2. Simplified 17.44

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

      [Start] 38.84	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 38.84	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 38.84	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 38.84	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 38.84	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 38.84	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 17.44	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Recombined 2 regimes into one program.

4. Final simplification 18.75

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	43.9%
Cost	13973

\[\begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.4 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-172} \lor \neg \left(A \leq 2.5 \cdot 10^{-21}\right) \land A \leq 4.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	46.13%
Cost	13972

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -5 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.5 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	39.17%
Cost	13968

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;A \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-172}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	39.12%
Cost	13968

\[\begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.85 \cdot 10^{-173}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 5
Error	38.71%
Cost	13968

\[\begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-265}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 6
Error	41.79%
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-260}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-292}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	39.33%
Cost	13836

\[\begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-171}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	55.08%
Cost	13708

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.2 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	51.85%
Cost	13708

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -9.6 \cdot 10^{-266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-292}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	53.63%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	59.97%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	78.88%
Cost	13056

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

Reproduce

herbie shell --seed 2023090 
(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)))