ABCF->ab-angle angle

Average Error: 29.2 → 11.6

Time: 22.9s

Precision: binary64

Cost: 60489

Math

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

↓

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

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 (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) 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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / 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 <= -0.5) or not (t_0 <= 0.0):
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / 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 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / 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 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 * atan((0.5 * (B / A)))) / 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[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

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 25.9

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

   2. Simplified 8.6

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      Proof
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.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) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.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 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C))))) B)) (PI.f64))): 6 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, 6 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 51.0

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

   2. Simplified 51.0

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
      Proof
      (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.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) (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 B B) (*.f64 (-.f64 A C) (-.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 (Rewrite<= unpow2_binary64 (pow.f64 B 2)) (*.f64 (-.f64 A C) (-.f64 A C))))) B)) (PI.f64))): 6 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, 6 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 A around -inf 32.0

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 11.6

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

Alternatives

Alternative 1
Error	14.9
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -0.43:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2
Error	15.9
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+51}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+163}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3
Error	34.3
Cost	14764

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_3 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-251}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-283}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 4
Error	31.5
Cost	14633

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := t_0 \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-251}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.36 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-175} \lor \neg \left(B \leq 1.3 \cdot 10^{-144}\right) \land B \leq 1.3 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 5
Error	27.6
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi \cdot 0.005555555555555556}\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -4.1 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq -8.5 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;C \leq 7.8 \cdot 10^{-20}:\\ \;\;\;\;t_1 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 16000000000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 6
Error	34.3
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2 \cdot 10^{+15}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.08 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{+62}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Error	34.3
Cost	14368

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := t_0 \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -5.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8
Error	28.2
Cost	14236

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq -5.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;C \leq 1.3 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;t_0 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 7800000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 9
Error	28.5
Cost	14236

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq -4.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;t_0 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 10
Error	25.2
Cost	14232

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-257}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	23.3
Cost	14232

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 12
Error	23.2
Cost	14232

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	25.3
Cost	14168

\[\begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -3.9 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.95 \cdot 10^{-258}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14
Error	34.3
Cost	13712

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.95 \cdot 10^{+45}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15
Error	34.3
Cost	13712

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	33.8
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-209}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 17
Error	34.0
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{+45}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	38.3
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Error	50.8
Cost	13056

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

Reproduce

herbie shell --seed 2022340 
(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)))