ABCF->ab-angle angle

Average Error: 29.5 → 13.8

Time: 22.7s

Precision: binary64

Cost: 20104

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;A \leq -92353448501550900:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.1364673988826312 \cdot 10^{-39}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \end{array} \]

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 -92353448501550900.0)
   (/ (atan (/ -0.5 (/ (- C A) B))) (* PI 0.005555555555555556))
   (if (<= A 1.1364673988826312e-39)
     (* (atan (/ (- C (hypot B C)) B)) (/ 180.0 PI))
     (* (/ 180.0 PI) (atan (/ (- (- A) (hypot A B)) B))))))

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 <= -92353448501550900.0) {
		tmp = atan((-0.5 / ((C - A) / B))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 1.1364673988826312e-39) {
		tmp = atan(((C - hypot(B, C)) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((-A - hypot(A, B)) / B));
	}
	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 <= -92353448501550900.0) {
		tmp = Math.atan((-0.5 / ((C - A) / B))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 1.1364673988826312e-39) {
		tmp = Math.atan(((C - Math.hypot(B, C)) / B)) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((-A - Math.hypot(A, B)) / B));
	}
	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 <= -92353448501550900.0:
		tmp = math.atan((-0.5 / ((C - A) / B))) / (math.pi * 0.005555555555555556)
	elif A <= 1.1364673988826312e-39:
		tmp = math.atan(((C - math.hypot(B, C)) / B)) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((-A - math.hypot(A, B)) / B))
	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 <= -92353448501550900.0)
		tmp = Float64(atan(Float64(-0.5 / Float64(Float64(C - A) / B))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 1.1364673988826312e-39)
		tmp = Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)));
	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 <= -92353448501550900.0)
		tmp = atan((-0.5 / ((C - A) / B))) / (pi * 0.005555555555555556);
	elseif (A <= 1.1364673988826312e-39)
		tmp = atan(((C - hypot(B, C)) / B)) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((-A - hypot(A, B)) / B));
	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, -92353448501550900.0], N[(N[ArcTan[N[(-0.5 / N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.1364673988826312e-39], N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -92353448501550896

   1. Initial program 48.2

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

   2. Simplified 26.8

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

   3. Taylor expanded in B around 0 18.1

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

   4. Applied egg-rr 18.7

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

   if -92353448501550896 < A < 1.1364673988826312e-39

   1. Initial program 28.4

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

   2. Simplified 13.0

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

   3. Taylor expanded in A around 0 30.1

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

   4. Simplified 14.6

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

   if 1.1364673988826312e-39 < A

   1. Initial program 15.5

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

   2. Simplified 4.1

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

   3. Taylor expanded in C around 0 16.8

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

   4. Simplified 8.2

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

4. Final simplification 13.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -92353448501550900:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.1364673988826312 \cdot 10^{-39}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	15.8
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -92353448501550900:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.6723895053983433:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 2
Error	27.6
Cost	14872

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \left(1 + \frac{C \cdot 0.5}{B}\right) \cdot \frac{C}{B}\right)\\ t_1 := \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.6028011558113545 \cdot 10^{-306}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.4059078418562753 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.806007533294603 \cdot 10^{-79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{elif}\;B \leq 5.823479861413413 \cdot 10^{-30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{A} \cdot \left(B + \left(1 + \frac{C}{A}\right) \cdot \left(C \cdot \frac{B}{A}\right)\right)\right)\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	30.5
Cost	14632

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.5245972611889756 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.5597606075580256 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.512409006040795 \cdot 10^{-145}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.025063674427173 \cdot 10^{-182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.316897971347595 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.312830825718162 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	30.5
Cost	14632

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{t_0}{\pi \cdot 0.005555555555555556}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_4 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.5245972611889756 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -5.5597606075580256 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.512409006040795 \cdot 10^{-145}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -2.025063674427173 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -7.316897971347595 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.312830825718162 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	30.4
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := \frac{t_1}{\pi \cdot 0.005555555555555556}\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -4.5245972611889756 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -5.5597606075580256 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.512409006040795 \cdot 10^{-145}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq -2.025063674427173 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.0347824064036512 \cdot 10^{-267}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 6.312830825718162 \cdot 10^{-146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	28.9
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.991865208106097 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.4059078418562753 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.806007533294603 \cdot 10^{-79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{elif}\;B \leq 5.823479861413413 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	27.4
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \left(1 + \frac{C \cdot 0.5}{B}\right) \cdot \frac{C}{B}\right)\\ t_2 := \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;B \leq -1.2840996866798638 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.6028011558113545 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.4059078418562753 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.806007533294603 \cdot 10^{-79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{elif}\;B \leq 5.823479861413413 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.9376615606327886 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.2356263990225886 \cdot 10^{+173}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	31.9
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.9743919377080706 \cdot 10^{-114}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.158382569847097 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.3039365848222455 \cdot 10^{-67}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 5.967046815865086 \cdot 10^{+164}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \]

Alternative 9
Error	26.8
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.9743919377080706 \cdot 10^{-114}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 2.5276299508850654 \cdot 10^{-148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.925028242960414 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 5184730436186.457:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	28.7
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -5.048922016351855 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.0347824064036512 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.312830825718162 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	28.9
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -5.048922016351855 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -6.782567454223411 \cdot 10^{-172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.316897971347595 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.312830825718162 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	34.2
Cost	13712

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.6287552838579292 \cdot 10^{+32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.0347824064036512 \cdot 10^{-267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.3999982338757 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5.9 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 13
Error	31.6
Cost	13444

\[\begin{array}{l} \mathbf{if}\;B \leq 6.991865208106097 \cdot 10^{-277}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 7.3999982338757 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 14
Error	35.0
Cost	13320

\[\begin{array}{l} \mathbf{if}\;B \leq -5.5597606075580256 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.3999982338757 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 15
Error	45.6
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -5.5597606075580256 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \]

Alternative 16
Error	50.8
Cost	13056

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

Reproduce

herbie shell --seed 2022228 
(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)))