ABCF->ab-angle angle

Average Error: 29.2 → 7.0

Time: 24.6s

Precision: binary64

Cost: 60488

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.0002:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))

↓

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.0002)
     (/
      1.0
      (*
       (/ PI (atan (/ (- (- C A) (hypot (- C A) B)) B)))
       0.005555555555555556))
     (if (<= t_0 0.0)
       (/ (atan (/ (* B 0.5) (- A C))) (* PI 0.005555555555555556))
       (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- C A))) B)) PI))))))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}

↓

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.0002) {
		tmp = 1.0 / ((((double) M_PI) / atan((((C - A) - hypot((C - A), B)) / B))) * 0.005555555555555556);
	} else if (t_0 <= 0.0) {
		tmp = atan(((B * 0.5) / (A - C))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
}

↓

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.0002) {
		tmp = 1.0 / ((Math.PI / Math.atan((((C - A) - Math.hypot((C - A), B)) / B))) * 0.005555555555555556);
	} else if (t_0 <= 0.0) {
		tmp = Math.atan(((B * 0.5) / (A - C))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)

↓

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.0002:
		tmp = 1.0 / ((math.pi / math.atan((((C - A) - math.hypot((C - A), B)) / B))) * 0.005555555555555556)
	elif t_0 <= 0.0:
		tmp = math.atan(((B * 0.5) / (A - C))) / (math.pi * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (C - A))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end

↓

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.0002)
		tmp = Float64(1.0 / Float64(Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B))) * 0.005555555555555556));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / Float64(A - C))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
end

↓

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.0002)
		tmp = 1.0 / ((pi / atan((((C - A) - hypot((C - A), B)) / B))) * 0.005555555555555556);
	elseif (t_0 <= 0.0)
		tmp = atan(((B * 0.5) / (A - C))) / (pi * 0.005555555555555556);
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

↓

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.0002], N[(1.0 / N[(N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 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]]]]

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))))) < -2.0000000000000001e-4

   1. Initial program 25.5

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

   2. Simplified 7.8

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 91 points increase in error, 21 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 10.6

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

   4. Applied egg-rr 7.8

      \[\leadsto \frac{1}{\color{blue}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)} \cdot 0.005555555555555556}} \]

   if -2.0000000000000001e-4 < (*.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 52.8

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

   2. Simplified 51.9

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 91 points increase in error, 21 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. Taylor expanded in B around 0 1.4

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

   4. Taylor expanded in C around -inf 1.4

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

   5. Simplified 1.3

      \[\leadsto \color{blue}{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right) \cdot \frac{180}{\pi}} \]
      Proof
      (*.f64 (atan.f64 (*.f64 1/2 (/.f64 B (-.f64 A C)))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 1/2 (/.f64 B (Rewrite<= unsub-neg_binary64 (+.f64 A (neg.f64 C)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 1/2 (/.f64 B (+.f64 A (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1/2 B) (+.f64 A (*.f64 -1 C))))) (/.f64 180 (PI.f64))): 0 points increase in error, 2 points decrease in error
      (*.f64 (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 -1 C) A)))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (/.f64 (*.f64 1/2 B) (+.f64 (*.f64 -1 C) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 A)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (/.f64 (*.f64 1/2 B) (+.f64 (*.f64 -1 C) (neg.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 -1 C) (*.f64 -1 A))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 C A))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 1/2 -1) (/.f64 B (-.f64 C A))))) (/.f64 180 (PI.f64))): 2 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 (Rewrite=> metadata-eval -1/2) (/.f64 B (-.f64 C A)))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A)))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B (Rewrite<= sub-neg_binary64 (-.f64 C A))))) (/.f64 180 (PI.f64))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (*.f64 -1/2 (/.f64 B (-.f64 C A)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 -1/2 (/.f64 B (-.f64 C A))))))): 25 points increase in error, 19 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 -1/2 (/.f64 B (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A)))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 -1/2 (/.f64 B (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A)))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 (Rewrite<= metadata-eval (/.f64 1/2 -1)) (/.f64 B (+.f64 C (*.f64 -1 A))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 (/.f64 1/2 -1) (/.f64 B (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A)))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (*.f64 (/.f64 1/2 -1) (/.f64 B (Rewrite<= sub-neg_binary64 (-.f64 C A))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 1/2 B) (*.f64 -1 (-.f64 C A))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 C) (*.f64 -1 A))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1 C) (neg.f64 (*.f64 -1 A)))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (*.f64 1/2 B) (+.f64 (*.f64 -1 C) (neg.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 A)))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (*.f64 1/2 B) (+.f64 (*.f64 -1 C) (Rewrite=> remove-double-neg_binary64 A)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (*.f64 1/2 B) (Rewrite<= +-commutative_binary64 (+.f64 A (*.f64 -1 C))))))): 0 points increase in error, 0 points decrease in error
      (/.f64 180 (/.f64 (PI.f64) (atan.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C)))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C)))))) (PI.f64))): 29 points increase in error, 26 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C))))) (PI.f64)))): 27 points increase in error, 29 points decrease in error

   6. Applied egg-rr 1.2

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A - C}\right)}{\pi \cdot 0.005555555555555556}} \]

   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 26.1

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

   2. Simplified 7.8

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 91 points increase in error, 21 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. Recombined 3 regimes into one program.

4. Final simplification 7.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.0002:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	11.9
Cost	20428

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq 2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 10^{+56}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2
Error	15.4
Cost	20304

\[\begin{array}{l} t_0 := -180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -5 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{+56}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3
Error	15.2
Cost	20304

\[\begin{array}{l} t_0 := -180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -5.5 \cdot 10^{+143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 4
Error	25.4
Cost	14500

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.15 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.42 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 720000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 7000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	24.9
Cost	14500

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{+75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	26.1
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.3 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-221}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.25 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 3.4 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	26.1
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -6.2 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.3 \cdot 10^{-221}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.2 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 9.4 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	26.1
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.8 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.25 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.35 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.02 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 6.8 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	21.6
Cost	14348

\[\begin{array}{l} \mathbf{if}\;B \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{elif}\;B \leq -2.55 \cdot 10^{-232}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(1 + \frac{\frac{A \cdot \left(A \cdot 0.5\right)}{B}}{B}\right) - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-186}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	27.6
Cost	14104

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -0.0235:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.9 \cdot 10^{-151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 6.4 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	34.2
Cost	14040

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	35.1
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.45 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13
Error	33.7
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Error	30.3
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-186}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15
Error	21.7
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16
Error	21.4
Cost	13968

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	21.4
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-185}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{elif}\;B \leq -1.18 \cdot 10^{-234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	21.5
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.85 \cdot 10^{-184}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 10^{-185}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 19
Error	35.0
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20
Error	38.0
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21
Error	50.3
Cost	13056

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

Reproduce

herbie shell --seed 2022332 
(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)))