ABCF->ab-angle angle

Average Error: 46.01% → 17.47%

Time: 22.1s

Precision: binary64

Cost: 60488

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-9}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}}\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{A \cdot A} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

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
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -4e-9)
     (/ (* 180.0 (atan (/ 1.0 (/ B (- (- C A) (hypot (- A C) B)))))) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* 0.5 (+ (/ (* B C) (* A A)) (/ B A)))) 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 t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -4e-9) {
		tmp = (180.0 * atan((1.0 / (B / ((C - A) - hypot((A - C), B)))))) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((0.5 * (((B * C) / (A * A)) + (B / A)))) / ((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 t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -4e-9) {
		tmp = (180.0 * Math.atan((1.0 / (B / ((C - A) - Math.hypot((A - C), B)))))) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((0.5 * (((B * C) / (A * A)) + (B / A)))) / 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):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -4e-9:
		tmp = (180.0 * math.atan((1.0 / (B / ((C - A) - math.hypot((A - C), B)))))) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((0.5 * (((B * C) / (A * A)) + (B / A)))) / 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)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -4e-9)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(B / Float64(Float64(C - A) - hypot(Float64(A - C), B)))))) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(Float64(B * C) / Float64(A * A)) + Float64(B / A)))) / 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)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -4e-9)
		tmp = (180.0 * atan((1.0 / (B / ((C - A) - hypot((A - C), B)))))) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((0.5 * (((B * C) / (A * A)) + (B / A)))) / 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_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -4e-9], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(B / N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(N[(B * C), $MachinePrecision] / N[(A * A), $MachinePrecision]), $MachinePrecision] + N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.00000000000000025e-9

   1. Initial program 39.69

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

   2. Simplified 39.7

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

      [Start] 39.69	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 39.7	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 39.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 39.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 39.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Applied egg-rr 11.84

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

   if -4.00000000000000025e-9 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

   1. Initial program 81.51

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

   2. Simplified 80.64

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

      [Start] 81.51	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 81.51	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 81.51	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 81.51	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 81.51	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 81.51	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 80.64	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Taylor expanded in A around -inf 49.83

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

   4. Simplified 49.83

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

      [Start] 49.83	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      distribute-lft-out [=>] 49.83	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C \cdot B}{{A}^{2}} + \frac{B}{A}\right)\right)}}{\pi} \]
      *-commutative [=>] 49.83	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{\color{blue}{B \cdot C}}{{A}^{2}} + \frac{B}{A}\right)\right)}{\pi} \]
      unpow2 [=>] 49.83	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{\color{blue}{A \cdot A}} + \frac{B}{A}\right)\right)}{\pi} \]

   if -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 41.17

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

   2. Simplified 12.94

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

      [Start] 41.17	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 41.17	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 41.17	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 41.17	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 41.17	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 41.17	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 12.94	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Recombined 3 regimes into one program.

4. Final simplification 17.47

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -4 \cdot 10^{-9}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{A \cdot A} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	32.72%
Cost	20368

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.5 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.6 \cdot 10^{-196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{A \cdot A} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-127}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t_1 + -1\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	26.17%
Cost	20232

\[\begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+148}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - \frac{\mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{hypot}\left(A, B\right)}{-B} - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	26.14%
Cost	20168

\[\begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{+144}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - \frac{\mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	18.84%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	18.83%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \]

Alternative 6
Error	47.18%
Cost	14437

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -8.2 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 7.4 \cdot 10^{-122} \lor \neg \left(A \leq 1.4 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 7
Error	47.12%
Cost	14437

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -8.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{180 \cdot t_2}{\pi}\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-69}:\\ \;\;\;\;180 \cdot \frac{t_2}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-261}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-123} \lor \neg \left(A \leq 5.4 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 8
Error	62.11%
Cost	14304

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-200}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -4.8 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-211}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	42.88%
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.4 \cdot 10^{+108}:\\ \;\;\;\;\frac{180 \cdot t_2}{\pi}\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.15 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{t_2}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	40%
Cost	14232

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -5.4 \cdot 10^{+108}:\\ \;\;\;\;\frac{180 \cdot t_2}{\pi}\\ \mathbf{elif}\;A \leq -4.6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -7.7 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{t_2}{\pi}\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.25 \cdot 10^{-136}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	41.38%
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -8.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{180 \cdot t_2}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -5.8 \cdot 10^{+60}:\\ \;\;\;\;180 \cdot \frac{t_2}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	34.15%
Cost	14088

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{if}\;B \leq -5.3 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B \cdot C}{A \cdot A} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	51.85%
Cost	14040

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -2.7 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -3.05 \cdot 10^{-285}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14
Error	33.49%
Cost	13572

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 5 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \]

Alternative 15
Error	52.05%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 75000000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	52.02%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17
Error	55.07%
Cost	13320

\[\begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	70.86%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq 3.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Error	79.05%
Cost	13056

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

Reproduce

herbie shell --seed 2023121 
(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)))