ABCF->ab-angle angle

Average Error: 29.6 → 17.6

Time: 27.0s

Precision: binary64

Cost: 54024

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(\frac{C}{B} - -1\right)\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C + B\right) - A\right)\right)}{\pi}\\ \end{array} \]

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
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -4e-5)
     (* 180.0 (/ (atan (+ (- -1.0 (+ 1.0 (/ A B))) (- (/ C B) -1.0))) PI))
     (if (<= t_0 4e-8)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (* 180.0 (/ (atan (* (/ 1.0 B) (- (+ C B) A))) 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 t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -4e-5) {
		tmp = 180.0 * (atan(((-1.0 - (1.0 + (A / B))) + ((C / B) - -1.0))) / ((double) M_PI));
	} else if (t_0 <= 4e-8) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C + B) - A))) / ((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 t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -4e-5) {
		tmp = 180.0 * (Math.atan(((-1.0 - (1.0 + (A / B))) + ((C / B) - -1.0))) / Math.PI);
	} else if (t_0 <= 4e-8) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C + B) - A))) / 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):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -4e-5:
		tmp = 180.0 * (math.atan(((-1.0 - (1.0 + (A / B))) + ((C / B) - -1.0))) / math.pi)
	elif t_0 <= 4e-8:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C + B) - A))) / 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)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -4e-5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-1.0 - Float64(1.0 + Float64(A / B))) + Float64(Float64(C / B) - -1.0))) / pi));
	elseif (t_0 <= 4e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C + B) - A))) / 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)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -4e-5)
		tmp = 180.0 * (atan(((-1.0 - (1.0 + (A / B))) + ((C / B) - -1.0))) / pi);
	elseif (t_0 <= 4e-8)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C + B) - A))) / 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_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -4e-5], N[(180.0 * N[(N[ArcTan[N[(N[(-1.0 - N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(C / B), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e-8], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.00000000000000033e-5

   1. Initial program 25.9

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

   2. Taylor expanded in B around inf 15.8

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

   3. Applied egg-rr 15.8

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

   4. Simplified 15.8

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

      [Start] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(1 - \frac{C}{-B}\right)\right)}{\pi} \]
      rational.json-simplify-8 [=>] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(1 - \frac{C}{\color{blue}{B \cdot -1}}\right)\right)}{\pi} \]
      rational.json-simplify-46 [=>] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(1 - \color{blue}{\frac{\frac{C}{B}}{-1}}\right)\right)}{\pi} \]
      rational.json-simplify-10 [<=] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(1 - \color{blue}{\left(-\frac{C}{B}\right)}\right)\right)}{\pi} \]
      rational.json-simplify-12 [=>] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(1 - \color{blue}{\left(0 - \frac{C}{B}\right)}\right)\right)}{\pi} \]
      rational.json-simplify-45 [=>] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \color{blue}{\left(\frac{C}{B} - \left(0 - 1\right)\right)}\right)}{\pi} \]
      metadata-eval [=>] 15.8	\[ 180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(\frac{C}{B} - \color{blue}{-1}\right)\right)}{\pi} \]

   if -4.00000000000000033e-5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 4.0000000000000001e-8

   1. Initial program 52.7

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

   2. Taylor expanded in A around -inf 30.8

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

   if 4.0000000000000001e-8 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 26.1

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

   2. Taylor expanded in B around -inf 15.2

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

4. Final simplification 17.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -4 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(-1 - \left(1 + \frac{A}{B}\right)\right) + \left(\frac{C}{B} - -1\right)\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 4 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C + B\right) - A\right)\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.3
Cost	14496

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 9 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{+158}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A + \left(-A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	30.4
Cost	14496

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C + B\right) - A\right)\right)}{\pi}\\ \mathbf{if}\;C \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.25 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.3 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.3 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 5 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 14500000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.18 \cdot 10^{+157}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A + \left(-A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	23.5
Cost	14096

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A + \left(-A\right)}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C + B\right) - A\right)\right)}{\pi}\\ \mathbf{if}\;B \leq -2.3 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.68 \cdot 10^{-307}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	26.3
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -2 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	33.9
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -170000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Error	33.8
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -6000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Error	32.5
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	25.6
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	26.0
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	26.1
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -8.1 \cdot 10^{+43}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	33.5
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.7 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	29.9
Cost	13444

\[\begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	38.3
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Error	50.5
Cost	13056

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

Reproduce

herbie shell --seed 2023074 
(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)))