ABCF->ab-angle angle

Average Error: 29.6 → 17.5

Time: 20.5s

Precision: binary64

Cost: 53896

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;t_0 \leq 10^{-6}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

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
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* (atan (/ (- (- C B) A) B)) (/ 180.0 PI))
     (if (<= t_0 1e-6)
       (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
       (* 180.0 (/ (atan (/ (- (+ C B) A) 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 t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = atan((((C - B) - A) / B)) * (180.0 / ((double) M_PI));
	} else if (t_0 <= 1e-6) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C + B) - A) / 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 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 <= -0.5) {
		tmp = Math.atan((((C - B) - A) / B)) * (180.0 / Math.PI);
	} else if (t_0 <= 1e-6) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C + B) - A) / 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):
	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 <= -0.5:
		tmp = math.atan((((C - B) - A) / B)) * (180.0 / math.pi)
	elif t_0 <= 1e-6:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C + B) - A) / 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)
	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 <= -0.5)
		tmp = Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) * Float64(180.0 / pi));
	elseif (t_0 <= 1e-6)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / 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)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = atan((((C - B) - A) / B)) * (180.0 / pi);
	elseif (t_0 <= 1e-6)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C + B) - A) / 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_] := 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, -0.5], N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e-6], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $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))))) < -0.5

   1. Initial program 26.6

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

   2. Simplified 26.6

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

      [Start] 26.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      rational_best-simplify-55 [=>] 26.6	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      rational_best-simplify-1 [=>] 26.6	\[ \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \cdot \frac{1}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-55 [=>] 26.6	\[ \tan^{-1} \color{blue}{\left(1 \cdot \frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-1 [=>] 26.6	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B} \cdot 1\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-7 [=>] 26.6	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]

   3. Taylor expanded in B around inf 16.1

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

   4. Simplified 16.1

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

      [Start] 16.1	\[ \tan^{-1} \left(\frac{\left(C + -1 \cdot B\right) - A}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-59 [=>] 16.1	\[ \tan^{-1} \left(\frac{\color{blue}{\left(-1 \cdot B - \left(-C\right)\right)} - A}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-14 [=>] 16.1	\[ \tan^{-1} \left(\frac{\left(-1 \cdot B - \color{blue}{\left(0 - C\right)}\right) - A}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-51 [=>] 16.1	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - \left(0 - -1 \cdot B\right)\right)} - A}{B}\right) \cdot \frac{180}{\pi} \]
      metadata-eval [<=] 16.1	\[ \tan^{-1} \left(\frac{\left(C - \left(\color{blue}{\frac{0}{-1}} - -1 \cdot B\right)\right) - A}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-37 [=>] 16.1	\[ \tan^{-1} \left(\frac{\left(C - \color{blue}{\frac{B}{\frac{-1}{-1}}}\right) - A}{B}\right) \cdot \frac{180}{\pi} \]
      metadata-eval [=>] 16.1	\[ \tan^{-1} \left(\frac{\left(C - \frac{B}{\color{blue}{1}}\right) - A}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-8 [=>] 16.1	\[ \tan^{-1} \left(\frac{\left(C - \color{blue}{B}\right) - A}{B}\right) \cdot \frac{180}{\pi} \]

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 9.99999999999999955e-7

   1. Initial program 51.4

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

   2. Simplified 51.4

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

      [Start] 51.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      rational_best-simplify-55 [=>] 51.4	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      rational_best-simplify-1 [=>] 51.4	\[ \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \cdot \frac{1}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-55 [=>] 51.4	\[ \tan^{-1} \color{blue}{\left(1 \cdot \frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-1 [=>] 51.4	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B} \cdot 1\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-7 [=>] 51.4	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]

   3. Taylor expanded in A around -inf 31.1

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

   if 9.99999999999999955e-7 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 25.6

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

   2. Simplified 25.6

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

      [Start] 25.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      rational_best-simplify-55 [=>] 25.6	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      rational_best-simplify-1 [=>] 25.6	\[ \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \cdot \frac{1}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-55 [=>] 25.6	\[ \tan^{-1} \color{blue}{\left(1 \cdot \frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-1 [=>] 25.6	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B} \cdot 1\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-7 [=>] 25.6	\[ \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}{B}\right)} \cdot \frac{180}{\pi} \]
      rational_best-simplify-52 [=>] 25.6	\[ \tan^{-1} \left(\frac{\color{blue}{C - \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}} + A\right)}}{B}\right) \cdot \frac{180}{\pi} \]
      rational_best-simplify-3 [=>] 25.6	\[ \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   3. Taylor expanded in B around -inf 14.7

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

   4. Taylor expanded in C around 0 14.7

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

4. Final simplification 17.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 10^{-6}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.6
Cost	14896

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \tan^{-1} \left(\frac{-A}{B}\right) \cdot \frac{180}{\pi}\\ t_2 := \tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_4 := \tan^{-1} -1 \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -2 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-298}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1050000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 3.05 \cdot 10^{+80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	31.5
Cost	14896

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \tan^{-1} -1 \cdot \frac{180}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_3 := 180 \cdot \frac{t_2}{\pi}\\ t_4 := \tan^{-1} \left(\frac{-A}{B}\right) \cdot \frac{180}{\pi}\\ t_5 := \tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -1.7 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.32 \cdot 10^{-212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-267}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-298}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-90}:\\ \;\;\;\;t_2 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1400000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	33.9
Cost	14764

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := \tan^{-1} \left(\frac{-A}{B}\right) \cdot \frac{180}{\pi}\\ t_3 := \tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ t_4 := \tan^{-1} -1 \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-71}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Error	27.8
Cost	14236

\[\begin{array}{l} t_0 := \tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.04 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-269}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-251}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 3.1 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	27.9
Cost	14236

\[\begin{array}{l} t_0 := \tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(\frac{C + B}{B}\right)\\ \mathbf{if}\;C \leq -4.7 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.25 \cdot 10^{-62}:\\ \;\;\;\;t_1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6
Error	26.0
Cost	14232

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7.9 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.98 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 31000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	26.0
Cost	14232

\[\begin{array}{l} t_0 := \tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ t_2 := 180 \cdot \frac{t_1}{\pi}\\ \mathbf{if}\;A \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-216}:\\ \;\;\;\;t_1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 31000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	34.8
Cost	14040

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{0}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(\frac{-A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -3.8 \cdot 10^{-100}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-133}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} -1 \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 9
Error	34.1
Cost	14040

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{-A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{-71}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -2.15 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.52 \cdot 10^{-268}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-272}:\\ \;\;\;\;\tan^{-1} \left(\frac{0}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} -1 \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 10
Error	34.9
Cost	13844

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{0}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(\frac{C}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} -1 \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 11
Error	25.8
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -2.45 \cdot 10^{+23}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-216}:\\ \;\;\;\;\tan^{-1} \left(\frac{C + B}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 34000000000000:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{B - A}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 12
Error	35.5
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-99}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-178}:\\ \;\;\;\;\tan^{-1} \left(\frac{0}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} -1 \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 13
Error	38.4
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\tan^{-1} 1 \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} -1 \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 14
Error	50.8
Cost	13056

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

Reproduce

herbie shell --seed 2023100 
(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)))