ABCF->ab-angle angle

Average Error: 30.0 → 11.1

Time: 17.4s

Precision: binary64

Cost: 60489

Math

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

↓

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

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 (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (/ (* 180.0 (atan (/ (* B -0.5) C))) 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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / 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 <= -0.5) or not (t_0 <= 0.0):
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / 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 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / 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 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 * atan(((B * -0.5) / C))) / 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[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $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], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or -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 26.5

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

   2. Simplified 8.2

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

      [Start] 26.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 26.5	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 26.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 26.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 26.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 26.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 8.2	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   if -0.5 < (*.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 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 52.2

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

      [Start] 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	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 52.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 52.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 52.2	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in C around inf 40.7

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

   4. Simplified 40.7

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

      [Start] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      fma-def [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}\right)}{\pi} \]
      +-commutative [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{\left({A}^{2} + {B}^{2}\right)} - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      associate--l+ [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{{A}^{2} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      unpow2 [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{\color{blue}{A \cdot A} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      unpow2 [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(\color{blue}{B \cdot B} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      mul-1-neg [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\color{blue}{\left(-A\right)}}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)\right)}{\pi} \]
      distribute-rgt1-in [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)\right)}{\pi} \]
      associate-*r* [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}\right)\right)}{\pi} \]
      metadata-eval [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \left(-1 \cdot \color{blue}{0}\right) \cdot A\right)\right)}{\pi} \]
      metadata-eval [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{0} \cdot A\right)\right)}{\pi} \]
      metadata-eval [<=] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{\left(-1 + 1\right)} \cdot A\right)\right)}{\pi} \]
      *-commutative [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{A \cdot \left(-1 + 1\right)}\right)\right)}{\pi} \]
      metadata-eval [=>] 40.7	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{C}, A \cdot \color{blue}{0}\right)\right)}{\pi} \]

   5. Taylor expanded in B around 0 29.6

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

   6. Simplified 29.6

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

      [Start] 29.6	\[ \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi} \]
      associate-*r/ [=>] 29.6	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]

3. Recombined 2 regimes into one program.

4. Final simplification 11.1

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

Alternatives

Alternative 1
Error	22.4
Cost	14348

\[\begin{array}{l} \mathbf{if}\;B \leq 4.8 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-124}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{A - C} + \frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{-\pi} \cdot \left(\tan^{-1} \left(\frac{C - A}{B} + -1\right) \cdot -180\right)\\ \end{array} \]

Alternative 2
Error	27.5
Cost	14236

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -1.42 \cdot 10^{+60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.7 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.4 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	31.9
Cost	14105

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -1 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-281} \lor \neg \left(B \leq 2.9 \cdot 10^{-210}\right) \land B \leq 1.2 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	33.6
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 17500000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Error	26.8
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.16 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -9.6 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6
Error	26.8
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.3 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -4.3 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	26.2
Cost	13968

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -2.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	26.2
Cost	13968

\[\begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq -9 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-178}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	26.2
Cost	13968

\[\begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{-\pi} \cdot \left(\tan^{-1} \left(\frac{C - A}{B} + -1\right) \cdot -180\right)\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	33.3
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	27.2
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -5.3 \cdot 10^{+60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.4 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	34.8
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.42 \cdot 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13
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 14
Error	50.6
Cost	13056

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

Reproduce

herbie shell --seed 2023187 
(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)))