ABCF->ab-angle angle

Average Error: 29.7 → 7.4

Time: 23.6s

Precision: binary64

Cost: 60616

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\pi \cdot \frac{-0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}}\\ \end{array} \]

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
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -4e-37)
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- C A))) B)) PI))
     (if (<= t_0 0.0)
       (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0))
       (/
        -1.0
        (*
         PI
         (/
          -0.005555555555555556
          (atan (/ (- (- C A) (hypot (- C A) B)) B)))))))))

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-37) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	} else {
		tmp = -1.0 / (((double) M_PI) * (-0.005555555555555556 / atan((((C - A) - hypot((C - A), B)) / B))));
	}
	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-37) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	} else {
		tmp = -1.0 / (Math.PI * (-0.005555555555555556 / Math.atan((((C - A) - Math.hypot((C - A), B)) / B))));
	}
	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-37:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (C - A))) / B)) / math.pi)
	elif t_0 <= 0.0:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	else:
		tmp = -1.0 / (math.pi * (-0.005555555555555556 / math.atan((((C - A) - math.hypot((C - A), B)) / B))))
	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-37)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	else
		tmp = Float64(-1.0 / Float64(pi * Float64(-0.005555555555555556 / atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B)))));
	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-37)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / pi);
	elseif (t_0 <= 0.0)
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	else
		tmp = -1.0 / (pi * (-0.005555555555555556 / atan((((C - A) - hypot((C - A), B)) / B))));
	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-37], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(Pi * N[(-0.005555555555555556 / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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))))) < -4.00000000000000027e-37

   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. Simplified 8.4

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      Proof
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 C A) (-.f64 C A)))))) B)) (PI.f64))): 96 points increase in error, 12 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 C A) (-.f64 C A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= sqr-neg_binary64 (*.f64 (neg.f64 (-.f64 C A)) (neg.f64 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 A C)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub-neg_binary64 (-.f64 A C)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (PI.f64))): 1 points increase in error, 0 points decrease in error

   if -4.00000000000000027e-37 < (*.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 51.6

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

   2. Simplified 51.3

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      Proof
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 C A) (-.f64 C A)))))) B)) (PI.f64))): 96 points increase in error, 12 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 C A) (-.f64 C A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= sqr-neg_binary64 (*.f64 (neg.f64 (-.f64 C A)) (neg.f64 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 A C)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub-neg_binary64 (-.f64 A C)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (PI.f64))): 1 points increase in error, 0 points decrease in error

   3. Applied egg-rr 55.8

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

   4. Simplified 55.8

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(C - A, B\right)\right)}{B}\right)}{\frac{\pi}{180}}} \]
      Proof
      (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 (-.f64 C A) B))) B)) (/.f64 (PI.f64) 180)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 (-.f64 C A) B))) B)) (PI.f64)) 180)): 4 points increase in error, 3 points decrease in error
      (Rewrite<= +-lft-identity_binary64 (+.f64 0 (*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 (-.f64 C A) B))) B)) (PI.f64)) 180))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in B around 0 0.6

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

   6. Applied egg-rr 0.6

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

   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 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 8.5

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      Proof
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 C A) (-.f64 C A)))))) B)) (PI.f64))): 96 points increase in error, 12 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 C A) (-.f64 C A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= sqr-neg_binary64 (*.f64 (neg.f64 (-.f64 C A)) (neg.f64 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 A C)) (neg.f64 (-.f64 C A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 C A))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 C) A)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 C)) A))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= +-commutative_binary64 (+.f64 A (neg.f64 C))))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (*.f64 (-.f64 A C) (Rewrite<= sub-neg_binary64 (-.f64 A C)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 B 2) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 A C) 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) B)) (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 180 (/.f64 (atan.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (PI.f64))): 1 points increase in error, 0 points decrease in error

   3. Applied egg-rr 11.6

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

   4. Applied egg-rr 8.5

      \[\leadsto \color{blue}{-1 \cdot \frac{1}{\left(-\pi\right) \cdot \frac{0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 7.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -4 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\pi \cdot \frac{-0.005555555555555556}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Error	11.6
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 2
Error	14.9
Cost	20040

\[\begin{array}{l} \mathbf{if}\;C \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 3
Error	13.6
Cost	20040

\[\begin{array}{l} \mathbf{if}\;C \leq -8 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 4
Error	33.8
Cost	14632

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.04 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.9 \cdot 10^{-98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.3 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 3.65 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	25.2
Cost	14628

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_3 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{if}\;C \leq -3.3 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-48}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;C \leq -1.8 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-257}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	33.9
Cost	14568

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 4.7 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	24.2
Cost	14496

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.85 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-241}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 58000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	24.3
Cost	14496

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -6.8 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1800000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	24.3
Cost	14496

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -5.9 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-245}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-183}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	24.3
Cost	14496

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.8 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-240}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-182}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1800000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	24.7
Cost	14364

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.1 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.75 \cdot 10^{-50}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;C \leq -2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.5 \cdot 10^{-257}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	31.5
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -0.000115:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -6.5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3.2 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.08 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	26.1
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.2 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 14
Error	25.9
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 15
Error	25.8
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_2 := \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{if}\;C \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -2.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;C \leq -2 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -3.2 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 16
Error	34.2
Cost	13712

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-289}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17
Error	34.5
Cost	13712

\[\begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	27.3
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2050000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19
Error	26.0
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.12 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20
Error	26.0
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 21
Error	35.7
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.04 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22
Error	38.6
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 23
Error	50.6
Cost	13056

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

Reproduce

herbie shell --seed 2022325 
(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)))