ABCF->ab-angle angle

Average Error: 29.2 → 12.9

Time: 19.2s

Precision: binary64

Cost: 20429

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;C \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - \mathsf{hypot}\left(A - C, B\right)\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{+43} \lor \neg \left(C \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)\\ \end{array} \]

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 (<= C 4.4e-27)
   (/ (* 180.0 (atan (* (/ 1.0 B) (- (- C (hypot (- A C) B)) A)))) PI)
   (if (or (<= C 5.5e+43) (not (<= C 2.6e+95)))
     (* (/ 180.0 PI) (atan (* (/ B C) -0.5)))
     (* (/ 180.0 PI) (atan (/ (- (- C A) (hypot B (- A C))) 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 (C <= 4.4e-27) {
		tmp = (180.0 * atan(((1.0 / B) * ((C - hypot((A - C), B)) - A)))) / ((double) M_PI);
	} else if ((C <= 5.5e+43) || !(C <= 2.6e+95)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B / C) * -0.5));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) - hypot(B, (A - C))) / 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 (C <= 4.4e-27) {
		tmp = (180.0 * Math.atan(((1.0 / B) * ((C - Math.hypot((A - C), B)) - A)))) / Math.PI;
	} else if ((C <= 5.5e+43) || !(C <= 2.6e+95)) {
		tmp = (180.0 / Math.PI) * Math.atan(((B / C) * -0.5));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) - Math.hypot(B, (A - C))) / 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 C <= 4.4e-27:
		tmp = (180.0 * math.atan(((1.0 / B) * ((C - math.hypot((A - C), B)) - A)))) / math.pi
	elif (C <= 5.5e+43) or not (C <= 2.6e+95):
		tmp = (180.0 / math.pi) * math.atan(((B / C) * -0.5))
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) - math.hypot(B, (A - C))) / 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 (C <= 4.4e-27)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(1.0 / B) * Float64(Float64(C - hypot(Float64(A - C), B)) - A)))) / pi);
	elseif ((C <= 5.5e+43) || !(C <= 2.6e+95))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B / C) * -0.5)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / 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 (C <= 4.4e-27)
		tmp = (180.0 * atan(((1.0 / B) * ((C - hypot((A - C), B)) - A)))) / pi;
	elseif ((C <= 5.5e+43) || ~((C <= 2.6e+95)))
		tmp = (180.0 / pi) * atan(((B / C) * -0.5));
	else
		tmp = (180.0 / pi) * atan((((C - A) - hypot(B, (A - C))) / 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[C, 4.4e-27], N[(N[(180.0 * N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[Or[LessEqual[C, 5.5e+43], N[Not[LessEqual[C, 2.6e+95]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < 4.39999999999999974e-27

   1. Initial program 23.1

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

   2. Simplified 23.1

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

      [Start] 23.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 23.1	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 23.1	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 23.1	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 23.1	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Applied egg-rr 9.3

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

   if 4.39999999999999974e-27 < C < 5.49999999999999989e43 or 2.5999999999999999e95 < C

   1. Initial program 47.7

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

   2. Simplified 28.9

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

      [Start] 47.7	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 47.7	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 47.7	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 47.7	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Taylor expanded in C around inf 42.6

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

   4. Simplified 38.6

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

      [Start] 42.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B} + -1 \cdot \frac{A + -1 \cdot A}{B}\right) \]
      fma-def [=>] 42.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)} \]
      associate--l+ [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      unpow2 [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      unpow2 [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(\color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      mul-1-neg [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\color{blue}{\left(-A\right)}}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      *-commutative [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{\color{blue}{B \cdot C}}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right) \]
      associate-*r/ [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \color{blue}{\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}}\right)\right) \]
      distribute-rgt1-in [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)\right) \]
      associate-*r* [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}}{B}\right)\right) \]
      metadata-eval [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\left(-1 \cdot \color{blue}{0}\right) \cdot A}{B}\right)\right) \]
      metadata-eval [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{0} \cdot A}{B}\right)\right) \]
      metadata-eval [<=] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{\left(-1 + 1\right)} \cdot A}{B}\right)\right) \]
      *-commutative [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{A \cdot \left(-1 + 1\right)}}{B}\right)\right) \]
      metadata-eval [=>] 38.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{A \cdot \color{blue}{0}}{B}\right)\right) \]

   5. Taylor expanded in B around 0 22.6

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

   6. Simplified 22.6

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

      [Start] 22.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]
      *-commutative [=>] 22.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)} \]

   if 5.49999999999999989e43 < C < 2.5999999999999999e95

   1. Initial program 39.4

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

   2. Simplified 25.1

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

      [Start] 39.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 39.4	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 39.4	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 39.4	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 39.4	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 39.4	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 39.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 39.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 39.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 25.1	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

3. Recombined 3 regimes into one program.

4. Final simplification 12.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - \mathsf{hypot}\left(A - C, B\right)\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{+43} \lor \neg \left(C \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	12.9
Cost	20429

\[\begin{array}{l} \mathbf{if}\;C \leq 1.5 \cdot 10^{-27} \lor \neg \left(C \leq 3.9 \cdot 10^{+43}\right) \land C \leq 7.8 \cdot 10^{+95}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ \end{array} \]

Alternative 2
Error	33.1
Cost	14764

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot t_0\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ t_3 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -1.18 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -8.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-204}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 1.08 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	32.9
Cost	14632

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := \frac{180}{\pi} \cdot t_1\\ \mathbf{if}\;C \leq -4.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -1.85 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -1.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	32.9
Cost	14632

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := \frac{180}{\pi} \cdot t_1\\ \mathbf{if}\;C \leq -1.42 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -1.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;C \leq -4.3 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;C \leq 6.5 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;C \leq 5.3 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.1 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-104}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	30.7
Cost	14500

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot t_0\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ \mathbf{if}\;C \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.65 \cdot 10^{-186}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -1.05 \cdot 10^{-299}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;C \leq 6.8 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-104}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	35.9
Cost	14369

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ t_1 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;B \leq -2.6 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.85 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.1 \lor \neg \left(B \leq 1.15 \cdot 10^{+49}\right) \land B \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Error	25.6
Cost	14100

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{if}\;C \leq -8.6 \cdot 10^{-144}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -6.4 \cdot 10^{-170}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -1.5 \cdot 10^{-300}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.1 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)\\ \end{array} \]

Alternative 8
Error	34.5
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9
Error	34.5
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10
Error	38.5
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	50.5
Cost	13056

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

Reproduce

herbie shell --seed 2023054 
(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)))