ABCF->ab-angle angle

Average Error: 29.2 → 18.8

Time: 35.6s

Precision: binary64

Cost: 54024

Math

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

↓

\[\begin{array}{l} t_0 := {\left(A - C\right)}^{2}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{t_0 + {B}^{2}}\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \left(0.5 \cdot \frac{t_0}{B} + B\right)\right)\right)}{\pi}\\ \mathbf{elif}\;t_1 \leq 0.005:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}{\pi}\\ \end{array} \]

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 (pow (- A C) 2.0))
        (t_1 (* (/ 1.0 B) (- (- C A) (sqrt (+ t_0 (pow B 2.0)))))))
   (if (<= t_1 -2e-63)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (+ (* 0.5 (/ t_0 B)) B)))) PI))
     (if (<= t_1 0.005)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (* 180.0 (/ (atan (- (/ C B) (+ (/ A B) -1.0))) 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 = pow((A - C), 2.0);
	double t_1 = (1.0 / B) * ((C - A) - sqrt((t_0 + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e-63) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - ((0.5 * (t_0 / B)) + B)))) / ((double) M_PI));
	} else if (t_1 <= 0.005) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) - ((A / B) + -1.0))) / ((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 = Math.pow((A - C), 2.0);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((t_0 + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e-63) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - ((0.5 * (t_0 / B)) + B)))) / Math.PI);
	} else if (t_1 <= 0.005) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) - ((A / B) + -1.0))) / 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 = math.pow((A - C), 2.0)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((t_0 + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -2e-63:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - ((0.5 * (t_0 / B)) + B)))) / math.pi)
	elif t_1 <= 0.005:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) - ((A / B) + -1.0))) / 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(A - C) ^ 2.0
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64(t_0 + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -2e-63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - Float64(Float64(0.5 * Float64(t_0 / B)) + B)))) / pi));
	elseif (t_1 <= 0.005)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - Float64(Float64(A / B) + -1.0))) / 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 = (A - C) ^ 2.0;
	t_1 = (1.0 / B) * ((C - A) - sqrt((t_0 + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -2e-63)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - ((0.5 * (t_0 / B)) + B)))) / pi);
	elseif (t_1 <= 0.005)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) - ((A / B) + -1.0))) / 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[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(t$95$0 + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-63], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[(N[(0.5 * N[(t$95$0 / B), $MachinePrecision]), $MachinePrecision] + B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.005], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - N[(N[(A / B), $MachinePrecision] + -1.0), $MachinePrecision]), $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))))) < -2.00000000000000013e-63

   1. Initial program 26.1

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

   2. Taylor expanded in B around inf 18.2

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

   if -2.00000000000000013e-63 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0050000000000000001

   1. Initial program 52.0

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

   2. Simplified 56.5

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

      [Start] 52.0	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      rational.json-simplify-45 [=>] 56.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]

   3. Taylor expanded in A around -inf 32.3

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

   if 0.0050000000000000001 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 25.1

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

   2. Simplified 25.1

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

      [Start] 25.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      rational.json-simplify-45 [=>] 25.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]

   3. Taylor expanded in B around -inf 15.1

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

   4. Simplified 15.1

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

      [Start] 15.1	\[ 180 \cdot \frac{\tan^{-1} \left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}{\pi} \]
      rational.json-simplify-17 [=>] 15.1	\[ 180 \cdot \frac{\tan^{-1} \left(\color{blue}{\left(\frac{C}{B} - -1\right)} - \frac{A}{B}\right)}{\pi} \]
      rational.json-simplify-42 [=>] 15.1	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(\frac{C}{B} - \frac{A}{B}\right) - -1\right)}}{\pi} \]
      rational.json-simplify-45 [=>] 15.1	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}}{\pi} \]

3. Recombined 3 regimes into one program.

4. Final simplification 18.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -2 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \left(0.5 \cdot \frac{{\left(A - C\right)}^{2}}{B} + B\right)\right)\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0.005:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	26.3
Cost	21016

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}{\pi}\\ \mathbf{if}\;C \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{\frac{{A}^{2}}{B} \cdot 0.5 + \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.55 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(-B\right) \cdot \left(0.5 \cdot \left(\frac{A}{{C}^{2}} + \frac{1}{C}\right)\right)\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	26.1
Cost	20620

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}{\pi}\\ \mathbf{if}\;C \leq -1.1 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.4 \cdot 10^{-265}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{\frac{{A}^{2}}{B} \cdot 0.5 + \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	25.8
Cost	14360

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \left(\frac{A}{B} + -1\right)\right)}{\pi}\\ \mathbf{if}\;C \leq -9.5 \cdot 10^{+64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-236}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.02 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	27.6
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -150000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3.75 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -7.2 \cdot 10^{-219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	34.5
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -8.6 \cdot 10^{-219}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6
Error	34.3
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.2 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.55 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.45 \cdot 10^{-82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	26.7
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -490000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 270000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	27.6
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -8.4 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -32000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1300000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	34.5
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -1.95 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.4 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 0.0085:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	33.8
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-171}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	33.7
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	38.3
Cost	13188

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

Alternative 13
Error	50.6
Cost	13056

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

Reproduce

herbie shell --seed 2023077 
(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)))