ABCF->ab-angle angle

Average Error: 28.8 → 11.7

Time: 23.9s

Precision: binary64

Cost: 20429

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;A \leq -4.1 \cdot 10^{+142} \lor \neg \left(A \leq -2 \cdot 10^{+83}\right) \land A \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

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
 (if (or (<= A -4.1e+142) (and (not (<= A -2e+83)) (<= A -1.7e+51)))
   (/ (/ (atan (* 0.5 (/ B A))) 0.005555555555555556) PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) 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 tmp;
	if ((A <= -4.1e+142) || (!(A <= -2e+83) && (A <= -1.7e+51))) {
		tmp = (atan((0.5 * (B / A))) / 0.005555555555555556) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / 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 tmp;
	if ((A <= -4.1e+142) || (!(A <= -2e+83) && (A <= -1.7e+51))) {
		tmp = (Math.atan((0.5 * (B / A))) / 0.005555555555555556) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / 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):
	tmp = 0
	if (A <= -4.1e+142) or (not (A <= -2e+83) and (A <= -1.7e+51)):
		tmp = (math.atan((0.5 * (B / A))) / 0.005555555555555556) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / 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)
	tmp = 0.0
	if ((A <= -4.1e+142) || (!(A <= -2e+83) && (A <= -1.7e+51)))
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) / 0.005555555555555556) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / 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)
	tmp = 0.0;
	if ((A <= -4.1e+142) || (~((A <= -2e+83)) && (A <= -1.7e+51)))
		tmp = (atan((0.5 * (B / A))) / 0.005555555555555556) / pi;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / 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_] := If[Or[LessEqual[A, -4.1e+142], And[N[Not[LessEqual[A, -2e+83]], $MachinePrecision], LessEqual[A, -1.7e+51]]], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.09999999999999982e142 or -2.00000000000000006e83 < A < -1.69999999999999992e51

   1. Initial program 52.2

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

   2. Simplified 44.6

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

      [Start] 52.2	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 52.2	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 52.2	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 52.2	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 27.0

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

   4. Taylor expanded in A around -inf 16.3

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

   if -4.09999999999999982e142 < A < -2.00000000000000006e83 or -1.69999999999999992e51 < A

   1. Initial program 24.4

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

   2. Simplified 10.9

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

      [Start] 24.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 24.4	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 24.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 24.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 24.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 24.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 10.9	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Recombined 2 regimes into one program.

4. Final simplification 11.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.1 \cdot 10^{+142} \lor \neg \left(A \leq -2 \cdot 10^{+83}\right) \land A \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	34.2
Cost	15028

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_1 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.32 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 26000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	34.2
Cost	15028

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-217}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4400000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	34.3
Cost	15028

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.42 \cdot 10^{-11}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-283}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.46 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-134}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1350000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	34.3
Cost	15028

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.15 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-218}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 210000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.7 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.06 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	22.5
Cost	14488

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(1 + \frac{C}{A}\right)\right)\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	25.3
Cost	14360

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-82}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 10^{+18}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	26.0
Cost	14233

\[\begin{array}{l} \mathbf{if}\;A \leq -7.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{-83}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-251} \lor \neg \left(A \leq 1.35 \cdot 10^{-107}\right) \land A \leq 10^{+18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 8
Error	25.2
Cost	14232

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -4.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-255}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 5.1 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t_0 + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_0 + -1\right)\\ \end{array} \]

Alternative 9
Error	25.1
Cost	14232

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -4.6 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 10^{-130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 10
Error	31.7
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;A \leq -4.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.36 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.0
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;A \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	27.4
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{if}\;A \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 13
Error	27.4
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 14
Error	26.5
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -9.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-83}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 4 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 15
Error	34.1
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-191}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	34.1
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-92}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17
Error	34.1
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-91}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	37.9
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 19
Error	50.4
Cost	13056

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

Reproduce

herbie shell --seed 2023057 
(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)))