ABCF->ab-angle angle

Average Error: 29.6 → 7.0

Time: 22.0s

Precision: binary64

Cost: 60488

Math

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

↓

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_1 \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- C A))) B)) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.5)
     t_0
     (if (<= t_1 0.0) (/ (atan (/ (* B 0.5) (- A C))) (/ PI 180.0)) t_0))))

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 26.5

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

   2. Simplified 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))): 86 points increase in error, 11 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))): 0 points increase in error, 0 points decrease in error

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

   1. Initial program 49.7

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

   2. Simplified 48.7

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 86 points increase in error, 11 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))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in B around 0 1.9

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

   4. Applied egg-rr 2.5

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

   5. Taylor expanded in C around -inf 1.9

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

   6. Simplified 1.7

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\frac{\pi}{180}}} \]
      Proof
      (/.f64 (atan.f64 (/.f64 (*.f64 B 1/2) (-.f64 A C))) (/.f64 (PI.f64) 180)): 0 points increase in error, 0 points decrease in error
      (/.f64 (atan.f64 (/.f64 (*.f64 B 1/2) (Rewrite<= unsub-neg_binary64 (+.f64 A (neg.f64 C))))) (/.f64 (PI.f64) 180)): 0 points increase in error, 0 points decrease in error
      (/.f64 (atan.f64 (/.f64 (*.f64 B 1/2) (+.f64 A (Rewrite<= mul-1-neg_binary64 (*.f64 -1 C))))) (/.f64 (PI.f64) 180)): 0 points increase in error, 0 points decrease in error
      (/.f64 (atan.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 B (+.f64 A (*.f64 -1 C))) 1/2))) (/.f64 (PI.f64) 180)): 2 points increase in error, 0 points decrease in error
      (/.f64 (atan.f64 (Rewrite<= *-commutative_binary64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C)))))) (/.f64 (PI.f64) 180)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (atan.f64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C))))) 180) (PI.f64))): 18 points increase in error, 9 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 180 (atan.f64 (*.f64 1/2 (/.f64 B (+.f64 A (*.f64 -1 C))))))) (PI.f64)): 0 points increase in error, 0 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)))): 26 points increase in error, 17 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 7.0

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

Alternatives

Alternative 1
Error	15.3
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	34.8
Cost	14500

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.8 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 3
Error	34.8
Cost	14500

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-170}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-282}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 4
Error	34.8
Cost	14500

\[\begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-280}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-288}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Error	34.8
Cost	14500

\[\begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ t_1 := \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-171}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.12 \cdot 10^{-280}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Error	31.9
Cost	14368

\[\begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.32 \cdot 10^{-167}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-281}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-288}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-108}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	27.5
Cost	14368

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ t_2 := \frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.35 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -50000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8500000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	27.4
Cost	14368

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq -5.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.4 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-186}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 10^{-159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	23.5
Cost	14236

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ t_2 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	34.2
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	27.4
Cost	14104

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.04 \cdot 10^{+14}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{-186}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	21.7
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-192}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-283}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	21.7
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-283}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14
Error	21.7
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.15 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.35 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-283}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15
Error	21.7
Cost	13968

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.32 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-192}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-283}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-108}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16
Error	34.5
Cost	13580

\[\begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-281}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-121}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17
Error	34.3
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	37.7
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Error	50.5
Cost	13056

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

Reproduce

herbie shell --seed 2022330 
(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)))