ABCF->ab-angle angle

Average Error: 30.0 → 7.3

Time: 28.6s

Precision: binary64

Cost: 66952

Math

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

↓

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left({\left(\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}\right)}^{-1}\right)\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_1 \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 PI)
          (atan (pow (/ B (- (- C A) (hypot B (- C A)))) -1.0))))
        (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 2e-8) (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))) 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 / ((double) M_PI)) * atan(pow((B / ((C - A) - hypot(B, (C - A)))), -1.0));
	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 <= 2e-8) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} 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.PI) * Math.atan(Math.pow((B / ((C - A) - Math.hypot(B, (C - A)))), -1.0));
	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 <= 2e-8) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} 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.pi) * math.atan(math.pow((B / ((C - A) - math.hypot(B, (C - A)))), -1.0))
	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 <= 2e-8:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	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(Float64(180.0 / pi) * atan((Float64(B / Float64(Float64(C - A) - hypot(B, Float64(C - A)))) ^ -1.0)))
	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 <= 2e-8)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	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 / pi) * atan(((B / ((C - A) - hypot(B, (C - A)))) ^ -1.0));
	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 <= 2e-8)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	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[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[Power[N[(B / N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]], $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, 2e-8], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $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 2e-8 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 26.2

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

   2. Simplified 8.3

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 83 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))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in C around 0 11.2

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

   4. Simplified 11.2

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)} \]
      Proof
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (Rewrite=> associate--r+_binary64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) B))): 9 points increase in error, 20 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A))) (hypot.f64 B (-.f64 C A))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A))) (hypot.f64 B (-.f64 C A))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A))))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A))))) B))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))))): 2 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64))): 2 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A))) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (Rewrite<= sub-neg_binary64 (-.f64 C A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A))))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (Rewrite<= sub-neg_binary64 (-.f64 C A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A))))) B))) (PI.f64)): 20 points increase in error, 9 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))): 2 points increase in error, 3 points decrease in error

   5. Applied egg-rr 8.3

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 2e-8

   1. Initial program 52.7

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

   2. Simplified 51.4

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]
      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))): 83 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))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in C around 0 55.3

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

   4. Simplified 55.3

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)} \]
      Proof
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (Rewrite=> associate--r+_binary64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) B))): 9 points increase in error, 20 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A))) (hypot.f64 B (-.f64 C A))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A))) (hypot.f64 B (-.f64 C A))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (Rewrite=> sub-neg_binary64 (+.f64 C (neg.f64 A))))) B))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 180 (PI.f64)) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (Rewrite<= mul-1-neg_binary64 (*.f64 -1 A))))) B))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))))): 2 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (+.f64 C (*.f64 -1 A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64))): 2 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A))) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (Rewrite<= sub-neg_binary64 (-.f64 C A)) (hypot.f64 B (+.f64 C (*.f64 -1 A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (+.f64 C (Rewrite=> mul-1-neg_binary64 (neg.f64 A))))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (Rewrite<= sub-neg_binary64 (-.f64 C A)))) B))) (PI.f64)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 180 (atan.f64 (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A))))) B))) (PI.f64)): 20 points increase in error, 9 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))): 2 points increase in error, 3 points decrease in error

   5. Taylor expanded in B around 0 1.7

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

   6. Simplified 1.7

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

4. Final simplification 7.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left({\left(\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}\right)}^{-1}\right)\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 2 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left({\left(\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}\right)}^{-1}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	12.8
Cost	20428

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq 5.3557679976148616 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8.871362191308086 \cdot 10^{-14}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{B}{\frac{C - A}{B}}}{B}\right)\\ \mathbf{elif}\;C \leq 4.905457726721158 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \end{array} \]

Alternative 2
Error	12.4
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -2.3038208148902673 \cdot 10^{+143}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 3
Error	14.1
Cost	20104

\[\begin{array}{l} \mathbf{if}\;A \leq -2.3038208148902673 \cdot 10^{+143}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 7.437540700954018 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)\\ \end{array} \]

Alternative 4
Error	16.2
Cost	20040

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -2.3038208148902673 \cdot 10^{+143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 0.08834636330144717:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.103514810523188 \cdot 10^{+51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{elif}\;A \leq 2.2047194690229718 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	30.2
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ t_1 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.988196805233329 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 6
Error	30.2
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ t_1 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.988196805233329 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 7
Error	30.3
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 8.988196805233329 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 8
Error	30.3
Cost	14104

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + C}{B}\right)\\ \mathbf{if}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 8.988196805233329 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 9
Error	29.1
Cost	13972

\[\begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -5.245729802797456 \cdot 10^{-214}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B + C}{B}\right)}}\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5581175485974017 \cdot 10^{-308}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.154572559926755 \cdot 10^{-277}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 5.669990659356278 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 10
Error	24.0
Cost	13972

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{if}\;B \leq 4.8606582137057714 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.2903029559082716 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.0109293891615249 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 11
Error	22.4
Cost	13968

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{if}\;B \leq 4.8606582137057714 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.2903029559082716 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.0109293891615249 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	22.7
Cost	13968

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{if}\;B \leq 4.8606582137057714 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.6866957816120064 \cdot 10^{-72}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\frac{B \cdot B}{C - A}}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.0109293891615249 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.959669127943071 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	34.1
Cost	13844

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.805175767864485 \cdot 10^{+20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Error	31.3
Cost	13844

\[\begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -5.245729802797456 \cdot 10^{-214}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B + C}{B}\right)}}\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5581175485974017 \cdot 10^{-308}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.154572559926755 \cdot 10^{-277}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15
Error	29.3
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;B \leq -2.3707615772378038 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.165542362837257 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -1.1509695741188392 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.669990659356278 \cdot 10^{-113}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 16
Error	34.0
Cost	13712

\[\begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{if}\;B \leq -3.519768527453808 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.5581175485974017 \cdot 10^{-308}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.154572559926755 \cdot 10^{-277}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17
Error	26.2
Cost	13576

\[\begin{array}{l} \mathbf{if}\;A \leq -2.789160791477636 \cdot 10^{+47}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 7.864949600245575 \cdot 10^{-19}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B + C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 18
Error	24.0
Cost	13572

\[\begin{array}{l} \mathbf{if}\;B \leq 23.46892183361177:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 19
Error	33.9
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -3.519768527453808 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 23.46892183361177:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20
Error	38.3
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -3.7081442106236837 \cdot 10^{-308}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21
Error	50.9
Cost	13056

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

Reproduce

herbie shell --seed 2022297 
(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)))