ABCF->ab-angle angle

Percentage Accurate: 54.2% → 89.3%

Time: 27.1s

Precision: binary64

Cost: 60489

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-68} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

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 -2e-68) (not (<= t_0 0.0)))
     (* (atan (/ (- (- C A) (hypot B (- C A))) B)) (/ 180.0 PI))
     (/ (atan (/ B (* (- C A) -2.0))) (* PI 0.005555555555555556)))))

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 <= -2e-68) || !(t_0 <= 0.0)) {
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = atan((B / ((C - A) * -2.0))) / (((double) M_PI) * 0.005555555555555556);
	}
	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 <= -2e-68) || !(t_0 <= 0.0)) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) * (180.0 / Math.PI);
	} else {
		tmp = Math.atan((B / ((C - A) * -2.0))) / (Math.PI * 0.005555555555555556);
	}
	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 <= -2e-68) or not (t_0 <= 0.0):
		tmp = math.atan((((C - A) - math.hypot(B, (C - A))) / B)) * (180.0 / math.pi)
	else:
		tmp = math.atan((B / ((C - A) * -2.0))) / (math.pi * 0.005555555555555556)
	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 <= -2e-68) || !(t_0 <= 0.0))
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) * -2.0))) / Float64(pi * 0.005555555555555556));
	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 <= -2e-68) || ~((t_0 <= 0.0)))
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / pi);
	else
		tmp = atan((B / ((C - A) * -2.0))) / (pi * 0.005555555555555556);
	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, -2e-68], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $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))))) < -2.00000000000000013e-68 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 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 86.1%

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

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

   if -2.00000000000000013e-68 < (*.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 23.8%

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

   2. Simplified 23.8%

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

      [Start] 23.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 23.8	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 23.8	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 23.8	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]

   3. Taylor expanded in B around 0 99.6%

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

   4. Simplified 99.6%

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

      [Start] 99.6	\[ \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi} \]
      *-commutative [=>] 99.6	\[ \tan^{-1} \color{blue}{\left(\frac{B}{C - A} \cdot -0.5\right)} \cdot \frac{180}{\pi} \]
      associate-*l/ [=>] 99.6	\[ \tan^{-1} \color{blue}{\left(\frac{B \cdot -0.5}{C - A}\right)} \cdot \frac{180}{\pi} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}} \]
      Step-by-step derivation

      [Start] 99.6	\[ \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right) \cdot \frac{180}{\pi} \]
      clear-num [=>] 99.6	\[ \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right) \cdot \color{blue}{\frac{1}{\frac{\pi}{180}}} \]
      un-div-inv [=>] 99.7	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}} \]
      associate-/l* [=>] 99.7	\[ \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C - A}{-0.5}}\right)}}{\frac{\pi}{180}} \]
      div-inv [=>] 99.7	\[ \frac{\tan^{-1} \left(\frac{B}{\color{blue}{\left(C - A\right) \cdot \frac{1}{-0.5}}}\right)}{\frac{\pi}{180}} \]
      metadata-eval [=>] 99.7	\[ \frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot \color{blue}{-2}}\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 99.7	\[ \frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]
      metadata-eval [=>] 99.7	\[ \frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -2 \cdot 10^{-68} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	75.1%
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -1.85 \cdot 10^{+177}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{+44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2
Accuracy	47.2%
Cost	14764

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.18 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 3
Accuracy	47.2%
Cost	14764

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 4
Accuracy	47.3%
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.26 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.28 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 53000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	47.2%
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{if}\;B \leq -2.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.82 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Accuracy	47.2%
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.05 \cdot 10^{-96}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 21000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Accuracy	47.3%
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.04 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-273}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-218}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8
Accuracy	56.9%
Cost	14497

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -1.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-229} \lor \neg \left(B \leq 6.2 \cdot 10^{+27}\right) \land B \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 9
Accuracy	56.9%
Cost	14497

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-226} \lor \neg \left(B \leq 7.2 \cdot 10^{+27}\right) \land B \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 10
Accuracy	56.9%
Cost	14497

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -4.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-227} \lor \neg \left(B \leq 4.1 \cdot 10^{+27}\right) \land B \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 11
Accuracy	59.8%
Cost	14497

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{if}\;A \leq -1.15 \cdot 10^{+142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.6 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-193}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-191} \lor \neg \left(A \leq 6.5 \cdot 10^{-102}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 12
Accuracy	59.8%
Cost	14497

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ t_1 := \frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;A \leq -1.15 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -6 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-192} \lor \neg \left(A \leq 1.22 \cdot 10^{-100}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 13
Accuracy	47.5%
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6800000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Accuracy	51.2%
Cost	14236

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;B \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-260}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.26 \cdot 10^{-272}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-238}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)\\ \mathbf{elif}\;B \leq 1.52 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 15
Accuracy	65.7%
Cost	14233

\[\begin{array}{l} t_0 := \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{if}\;B \leq -6.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;B \leq -1.18 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-233}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\left(C - A\right) \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;B \leq 8.7 \cdot 10^{+27} \lor \neg \left(B \leq 1.1 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \end{array} \]

Alternative 16
Accuracy	55.0%
Cost	13972

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-225}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 17
Accuracy	58.9%
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -1 \cdot 10^{-65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq -1.3 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{elif}\;C \leq 3.1 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 18
Accuracy	47.4%
Cost	13712

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-309}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Accuracy	47.6%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20
Accuracy	40.5%
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 21
Accuracy	20.7%
Cost	13056

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

Reproduce

herbie shell --seed 2023160 
(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)))