ABCF->ab-angle angle

Average Accuracy: 54.2% → 81.8%

Time: 17.8s

Precision: binary64

Cost: 20292

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;C \leq 1.15 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

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 (<= C 1.15e+151)
   (/
    1.0
    (/ (* PI 0.005555555555555556) (atan (/ (- (- C A) (hypot B (- A C))) B))))
   (* 180.0 (/ (atan (* B (/ -0.5 C))) 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 (C <= 1.15e+151) {
		tmp = 1.0 / ((((double) M_PI) * 0.005555555555555556) / atan((((C - A) - hypot(B, (A - C))) / B)));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((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 (C <= 1.15e+151) {
		tmp = 1.0 / ((Math.PI * 0.005555555555555556) / Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)));
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / 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 C <= 1.15e+151:
		tmp = 1.0 / ((math.pi * 0.005555555555555556) / math.atan((((C - A) - math.hypot(B, (A - C))) / B)))
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / 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 (C <= 1.15e+151)
		tmp = Float64(1.0 / Float64(Float64(pi * 0.005555555555555556) / atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / 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 (C <= 1.15e+151)
		tmp = 1.0 / ((pi * 0.005555555555555556) / atan((((C - A) - hypot(B, (A - C))) / B)));
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / 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[C, 1.15e+151], N[(1.0 / N[(N[(Pi * 0.005555555555555556), $MachinePrecision] / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.15e151

   1. Initial program 60.6%

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

   2. Simplified 76.9%

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

      [Start] 60.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 60.6	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 60.6	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 60.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 82.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

   if 1.15e151 < C

   1. Initial program 12.0%

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

   2. Simplified 12.0%

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

      [Start] 12.0	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 12.0	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 12.0	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 12.0	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 12.0	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in C around inf 47.9%

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

   4. Simplified 52.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, A \cdot 0\right)}\right)}{\pi} \]
      Proof

      [Start] 47.9	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      fma-def [=>] 47.9	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}\right)}{\pi} \]
      associate--l+ [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      unpow2 [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      unpow2 [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(\color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      mul-1-neg [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\color{blue}{\left(-A\right)}}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      distribute-rgt1-in [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)\right)}{\pi} \]
      associate-*r* [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}\right)\right)}{\pi} \]
      metadata-eval [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \left(-1 \cdot \color{blue}{0}\right) \cdot A\right)\right)}{\pi} \]
      metadata-eval [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{0} \cdot A\right)\right)}{\pi} \]
      metadata-eval [<=] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 + 1\right)} \cdot A\right)\right)}{\pi} \]
      *-commutative [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{A \cdot \left(-1 + 1\right)}\right)\right)}{\pi} \]
      metadata-eval [=>] 52.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, A \cdot \color{blue}{0}\right)\right)}{\pi} \]

   5. Taylor expanded in B around 0 79.0%

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

   6. Simplified 79.0%

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

      [Start] 79.0	\[ \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi} \]
      associate-*r/ [=>] 79.0	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]
      associate-/l* [=>] 78.0	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)}}{\pi} \]
      associate-/r/ [=>] 79.0	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   7. Applied egg-rr 78.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{C} \cdot B\right)}{\pi}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.15 \cdot 10^{+151}:\\ \;\;\;\;\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.7%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 2.1 \cdot 10^{+150}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 2
Accuracy	81.8%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 8.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 3
Accuracy	57.1%
Cost	14232

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{if}\;C \leq -5.7 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.05 \cdot 10^{-215}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.72 \cdot 10^{-298}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 7.4 \cdot 10^{-252}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right)\\ \mathbf{elif}\;C \leq 10^{-110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{+124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 4
Accuracy	56.3%
Cost	14232

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ t_1 := \frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{if}\;C \leq -1.3 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -5.5 \cdot 10^{-304}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-252}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right)\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	45.9%
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Accuracy	48.0%
Cost	13972

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.4 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.05 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 0.0275:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Accuracy	59.8%
Cost	13968

\[\begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-276}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 3.3 \cdot 10^{-184}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \end{array} \]

Alternative 8
Accuracy	55.7%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right)\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-185}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Accuracy	55.8%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Accuracy	47.7%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -4.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Accuracy	40.2%
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 12
Accuracy	20.6%
Cost	13056

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

Reproduce

herbie shell --seed 2023141 
(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)))