ABCF->ab-angle angle

Average Error: 29.6 → 13.4

Time: 19.3s

Precision: binary64

Cost: 20428

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;A \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - t_0}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-103}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + t_0\right)}{B}\right)\\ \end{array} \]

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
 (let* ((t_0 (hypot B (- A C))))
   (if (<= A -3.5e+134)
     (/ (/ (atan (/ (* B 0.5) A)) 0.005555555555555556) PI)
     (if (<= A -9.2e-33)
       (* 180.0 (/ (atan (/ (- (- C A) t_0) B)) PI))
       (if (<= A -2.15e-103)
         (/ (* 180.0 (atan (* 0.5 (+ (/ B A) (/ B (/ A (/ C A))))))) PI)
         (* (/ 180.0 PI) (atan (/ (- C (+ A t_0)) 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 t_0 = hypot(B, (A - C));
	double tmp;
	if (A <= -3.5e+134) {
		tmp = (atan(((B * 0.5) / A)) / 0.005555555555555556) / ((double) M_PI);
	} else if (A <= -9.2e-33) {
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / ((double) M_PI));
	} else if (A <= -2.15e-103) {
		tmp = (180.0 * atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + t_0)) / 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 t_0 = Math.hypot(B, (A - C));
	double tmp;
	if (A <= -3.5e+134) {
		tmp = (Math.atan(((B * 0.5) / A)) / 0.005555555555555556) / Math.PI;
	} else if (A <= -9.2e-33) {
		tmp = 180.0 * (Math.atan((((C - A) - t_0) / B)) / Math.PI);
	} else if (A <= -2.15e-103) {
		tmp = (180.0 * Math.atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + t_0)) / 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):
	t_0 = math.hypot(B, (A - C))
	tmp = 0
	if A <= -3.5e+134:
		tmp = (math.atan(((B * 0.5) / A)) / 0.005555555555555556) / math.pi
	elif A <= -9.2e-33:
		tmp = 180.0 * (math.atan((((C - A) - t_0) / B)) / math.pi)
	elif A <= -2.15e-103:
		tmp = (180.0 * math.atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + t_0)) / 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)
	t_0 = hypot(B, Float64(A - C))
	tmp = 0.0
	if (A <= -3.5e+134)
		tmp = Float64(Float64(atan(Float64(Float64(B * 0.5) / A)) / 0.005555555555555556) / pi);
	elseif (A <= -9.2e-33)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - t_0) / B)) / pi));
	elseif (A <= -2.15e-103)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(B / Float64(A / Float64(C / A))))))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + t_0)) / 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)
	t_0 = hypot(B, (A - C));
	tmp = 0.0;
	if (A <= -3.5e+134)
		tmp = (atan(((B * 0.5) / A)) / 0.005555555555555556) / pi;
	elseif (A <= -9.2e-33)
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / pi);
	elseif (A <= -2.15e-103)
		tmp = (180.0 * atan((0.5 * ((B / A) + (B / (A / (C / A))))))) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (A + t_0)) / 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_] := Block[{t$95$0 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, If[LessEqual[A, -3.5e+134], N[(N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -9.2e-33], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.15e-103], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(B / N[(A / N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + t$95$0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -3.50000000000000003e134

   1. Initial program 54.6

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

   2. Simplified 47.7

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

      [Start] 54.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 54.6	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 54.6	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 54.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 27.8

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

   4. Taylor expanded in A around -inf 13.7

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

   5. Simplified 13.7

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

      [Start] 13.7	\[ \frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi} \]
      associate-*r/ [=>] 13.7	\[ \frac{\frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{0.005555555555555556}}{\pi} \]
      *-commutative [=>] 13.7	\[ \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{B \cdot 0.5}}{A}\right)}{0.005555555555555556}}{\pi} \]

   if -3.50000000000000003e134 < A < -9.19999999999999942e-33

   1. Initial program 37.8

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

   2. Simplified 25.1

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

      [Start] 37.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 37.8	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 37.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 37.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 37.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 37.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 25.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   if -9.19999999999999942e-33 < A < -2.15000000000000011e-103

   1. Initial program 32.4

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

   2. Simplified 32.4

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

      [Start] 32.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 32.4	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 32.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 32.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 32.4	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in A around -inf 40.8

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

   4. Simplified 40.8

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

      [Start] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      distribute-lft-out [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C \cdot B}{{A}^{2}} + \frac{B}{A}\right)\right)}}{\pi} \]
      +-commutative [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \color{blue}{\left(\frac{B}{A} + \frac{C \cdot B}{{A}^{2}}\right)}\right)}{\pi} \]
      *-commutative [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{\color{blue}{B \cdot C}}{{A}^{2}}\right)\right)}{\pi} \]
      associate-/l* [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \color{blue}{\frac{B}{\frac{{A}^{2}}{C}}}\right)\right)}{\pi} \]
      unpow2 [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{\color{blue}{A \cdot A}}{C}}\right)\right)}{\pi} \]
      associate-/l* [=>] 40.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\color{blue}{\frac{A}{\frac{C}{A}}}}\right)\right)}{\pi} \]

   if -2.15000000000000011e-103 < A

   1. Initial program 22.3

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

   2. Simplified 8.5

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

      [Start] 22.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 22.3	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 22.3	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 22.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 13.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-103}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	13.4
Cost	20429

\[\begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-33} \lor \neg \left(A \leq -2.15 \cdot 10^{-103}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	17.0
Cost	20304

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-103}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 3000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	26.2
Cost	14220

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.15 \cdot 10^{-217}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t_0\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	22.8
Cost	13968

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{if}\;B \leq -1.4 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{-\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	35.3
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Error	35.3
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Error	32.7
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{-257}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 8
Error	27.6
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 9
Error	27.6
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 10
Error	25.4
Cost	13572

\[\begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	38.5
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-303}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	50.8
Cost	13056

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

Reproduce

herbie shell --seed 2023066 
(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)))