ABCF->ab-angle angle

Average Error: 29.6 → 12.0

Time: 17.6s

Precision: binary64

Cost: 20164

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right) \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

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 (<= A -1.8e+91)
   (/ (* 180.0 (atan (* (* (/ B A) (+ (/ C A) 1.0)) 0.5))) 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 <= -1.8e+91) {
		tmp = (180.0 * atan((((B / A) * ((C / A) + 1.0)) * 0.5))) / ((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 <= -1.8e+91) {
		tmp = (180.0 * Math.atan((((B / A) * ((C / A) + 1.0)) * 0.5))) / 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 <= -1.8e+91:
		tmp = (180.0 * math.atan((((B / A) * ((C / A) + 1.0)) * 0.5))) / 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 <= -1.8e+91)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(B / A) * Float64(Float64(C / A) + 1.0)) * 0.5))) / 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 <= -1.8e+91)
		tmp = (180.0 * atan((((B / A) * ((C / A) + 1.0)) * 0.5))) / 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[LessEqual[A, -1.8e+91], N[(N[(180.0 * N[ArcTan[N[(N[(N[(B / A), $MachinePrecision] * N[(N[(C / A), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $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 < -1.8e91

   1. Initial program 51.2

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

   2. Simplified 51.2

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

      [Start] 51.2	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 51.2	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 51.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 51.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 51.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in A around -inf 18.8

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

   4. Simplified 18.8

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

      [Start] 18.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      distribute-lft-out [=>] 18.8	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C \cdot B}{{A}^{2}} + \frac{B}{A}\right)\right)}}{\pi} \]
      *-commutative [=>] 18.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{\color{blue}{B \cdot C}}{{A}^{2}} + \frac{B}{A}\right)\right)}{\pi} \]
      unpow2 [=>] 18.8	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{\color{blue}{A \cdot A}} + \frac{B}{A}\right)\right)}{\pi} \]

   5. Taylor expanded in B around 0 16.2

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

   6. Simplified 15.8

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

      [Start] 16.2	\[ \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\left(\frac{C}{{A}^{2}} + \frac{1}{A}\right) \cdot B\right)\right)}{\pi} \]
      *-commutative [=>] 16.2	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(\frac{C}{{A}^{2}} + \frac{1}{A}\right) \cdot B\right) \cdot 0.5\right)}}{\pi} \]
      *-commutative [=>] 16.2	\[ \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(B \cdot \left(\frac{C}{{A}^{2}} + \frac{1}{A}\right)\right)} \cdot 0.5\right)}{\pi} \]
      unpow2 [=>] 16.2	\[ \frac{180 \cdot \tan^{-1} \left(\left(B \cdot \left(\frac{C}{\color{blue}{A \cdot A}} + \frac{1}{A}\right)\right) \cdot 0.5\right)}{\pi} \]
      distribute-lft-in [=>] 16.2	\[ \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(B \cdot \frac{C}{A \cdot A} + B \cdot \frac{1}{A}\right)} \cdot 0.5\right)}{\pi} \]
      associate-*r/ [=>] 18.9	\[ \frac{180 \cdot \tan^{-1} \left(\left(\color{blue}{\frac{B \cdot C}{A \cdot A}} + B \cdot \frac{1}{A}\right) \cdot 0.5\right)}{\pi} \]
      *-commutative [=>] 18.9	\[ \frac{180 \cdot \tan^{-1} \left(\left(\frac{\color{blue}{C \cdot B}}{A \cdot A} + B \cdot \frac{1}{A}\right) \cdot 0.5\right)}{\pi} \]
      times-frac [=>] 15.8	\[ \frac{180 \cdot \tan^{-1} \left(\left(\color{blue}{\frac{C}{A} \cdot \frac{B}{A}} + B \cdot \frac{1}{A}\right) \cdot 0.5\right)}{\pi} \]
      associate-*r/ [=>] 15.8	\[ \frac{180 \cdot \tan^{-1} \left(\left(\frac{C}{A} \cdot \frac{B}{A} + \color{blue}{\frac{B \cdot 1}{A}}\right) \cdot 0.5\right)}{\pi} \]
      *-commutative [=>] 15.8	\[ \frac{180 \cdot \tan^{-1} \left(\left(\frac{C}{A} \cdot \frac{B}{A} + \frac{\color{blue}{1 \cdot B}}{A}\right) \cdot 0.5\right)}{\pi} \]
      associate-*r/ [<=] 15.8	\[ \frac{180 \cdot \tan^{-1} \left(\left(\frac{C}{A} \cdot \frac{B}{A} + \color{blue}{1 \cdot \frac{B}{A}}\right) \cdot 0.5\right)}{\pi} \]
      distribute-rgt-out [=>] 15.8	\[ \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right)} \cdot 0.5\right)}{\pi} \]

   if -1.8e91 < A

   1. Initial program 24.8

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

   2. Simplified 11.1

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

      [Start] 24.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 24.8	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 24.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 24.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 24.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 24.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 11.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Recombined 2 regimes into one program.

4. Final simplification 12.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right) \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.8
Cost	20497

\[\begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-179} \lor \neg \left(B \leq 1.85 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	27.0
Cost	14237

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -5 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.7 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 880000000 \lor \neg \left(A \leq 1.05 \cdot 10^{+124}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 3
Error	22.7
Cost	14225

\[\begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-303}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-176} \lor \neg \left(B \leq 1.02 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right) \cdot 0.5\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	34.5
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.15 \cdot 10^{-262}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Error	29.9
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	30.6
Cost	13840

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;A \leq -2 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.25 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.36 \cdot 10^{-260}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 8.8 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 7
Error	24.8
Cost	13837

\[\begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-88}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-262} \lor \neg \left(B \leq 1.2 \cdot 10^{-303}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \]

Alternative 8
Error	22.2
Cost	13704

\[\begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-263}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 9
Error	34.5
Cost	13512

\[\begin{array}{l} \mathbf{if}\;B \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10
Error	34.6
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	38.9
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	50.9
Cost	13056

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

Reproduce

herbie shell --seed 2023067 
(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)))