ABCF->ab-angle angle

Average Accuracy: 54.1% → 79.5%

Time: 17.2s

Precision: binary64

Cost: 20428

Math

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

↓

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;C \leq 4 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-208}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

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 (* (atan (/ (- (- C A) (hypot B (- A C))) B)) (/ 180.0 PI))))
   (if (<= C 4e-243)
     t_0
     (if (<= C 3.7e-208)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= C 1.45e+92) t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))))

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 = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / ((double) M_PI));
	double tmp;
	if (C <= 4e-243) {
		tmp = t_0;
	} else if (C <= 3.7e-208) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 1.45e+92) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	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.atan((((C - A) - Math.hypot(B, (A - C))) / B)) * (180.0 / Math.PI);
	double tmp;
	if (C <= 4e-243) {
		tmp = t_0;
	} else if (C <= 3.7e-208) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 1.45e+92) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	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.atan((((C - A) - math.hypot(B, (A - C))) / B)) * (180.0 / math.pi)
	tmp = 0
	if C <= 4e-243:
		tmp = t_0
	elif C <= 3.7e-208:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 1.45e+92:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	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(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) * Float64(180.0 / pi))
	tmp = 0.0
	if (C <= 4e-243)
		tmp = t_0;
	elseif (C <= 3.7e-208)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 1.45e+92)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	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 = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / pi);
	tmp = 0.0;
	if (C <= 4e-243)
		tmp = t_0;
	elseif (C <= 3.7e-208)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 1.45e+92)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	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[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, 4e-243], t$95$0, If[LessEqual[C, 3.7e-208], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.45e+92], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if C < 3.99999999999999998e-243 or 3.7000000000000002e-208 < C < 1.45e92

   1. Initial program 61.5%

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

   2. Simplified 82.6%

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

      [Start] 61.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 61.5	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 61.5	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 61.5	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 61.5	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 61.5	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 61.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 61.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 61.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 82.6	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   if 3.99999999999999998e-243 < C < 3.7000000000000002e-208

   1. Initial program 54.4%

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

   2. Simplified 80.9%

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

      [Start] 54.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 54.4	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 54.4	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 54.4	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 54.4	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 54.4	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 54.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 54.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 54.4	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 80.9	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   3. Taylor expanded in A around -inf 30.4%

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

   if 1.45e92 < C

   1. Initial program 19.4%

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

   2. Simplified 53.3%

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

      [Start] 19.4	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 19.4	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 19.4	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 19.4	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Taylor expanded in C around inf 45.9%

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

   4. Simplified 45.9%

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

      [Start] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}{B}\right) \]
      fma-def [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right) \]
      +-commutative [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\left({A}^{2} + {B}^{2}\right)} - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right) \]
      associate--l+ [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{A}^{2} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right) \]
      unpow2 [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{A \cdot A} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right) \]
      unpow2 [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(\color{blue}{B \cdot B} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right) \]
      mul-1-neg [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\color{blue}{\left(-A\right)}}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right) \]
      distribute-rgt1-in [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right) \]
      associate-*r* [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}\right)}{B}\right) \]
      metadata-eval [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \left(-1 \cdot \color{blue}{0}\right) \cdot A\right)}{B}\right) \]
      metadata-eval [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{0} \cdot A\right)}{B}\right) \]
      metadata-eval [<=] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 + 1\right)} \cdot A\right)}{B}\right) \]
      *-commutative [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{A \cdot \left(-1 + 1\right)}\right)}{B}\right) \]
      metadata-eval [=>] 45.9	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, A \cdot \color{blue}{0}\right)}{B}\right) \]

   5. Taylor expanded in A around 0 74.3%

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

   6. Simplified 74.3%

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

      [Start] 74.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]
      associate-*r/ [=>] 74.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)} \]
      *-commutative [=>] 74.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{B \cdot -0.5}}{C}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 4 \cdot 10^{-243}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-208}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{+92}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	56.5%
Cost	14368

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{\frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{0.005555555555555556}}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -3.8 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 70000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Accuracy	57.0%
Cost	14364

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{\frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{0.005555555555555556}}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) \cdot 2}{B}\right)}}\\ \end{array} \]

Alternative 3
Accuracy	58.0%
Cost	14100

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;C \leq -6.2 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.45 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi \cdot \frac{1}{t_1}}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-208}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 4
Accuracy	47.9%
Cost	13840

\[\begin{array}{l} \mathbf{if}\;C \leq -5.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{elif}\;C \leq -9.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-164}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]

Alternative 5
Accuracy	48.0%
Cost	13840

\[\begin{array}{l} \mathbf{if}\;C \leq -1.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -2.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]

Alternative 6
Accuracy	48.0%
Cost	13840

\[\begin{array}{l} \mathbf{if}\;C \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -1.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 7
Accuracy	52.0%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;C \leq -5.6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.15 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -4.4 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-208}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 8
Accuracy	55.8%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 42000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Accuracy	45.5%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{+39}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10
Accuracy	46.4%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Accuracy	40.0%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Accuracy	21.4%
Cost	13056

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

Reproduce

herbie shell --seed 2023129 
(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)))