ABCF->ab-angle angle

Average Error: 29.3 → 7.0

Time: 20.8s

Precision: binary64

Cost: 60488

Math

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

↓

\[\begin{array}{l} t_0 := \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_1 \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 (* (atan (/ (- (- C A) (hypot B (- C A))) B)) (/ 180.0 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 (* -0.5 (/ B (- C A)))) (* PI 0.005555555555555556))
       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 = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / ((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((-0.5 * (B / (C - A)))) / (((double) M_PI) * 0.005555555555555556);
	} 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 = Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) * (180.0 / 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((-0.5 * (B / (C - A)))) / (Math.PI * 0.005555555555555556);
	} 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 = math.atan((((C - A) - math.hypot(B, (C - A))) / B)) * (180.0 / 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((-0.5 * (B / (C - A)))) / (math.pi * 0.005555555555555556)
	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(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) * Float64(180.0 / 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(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi * 0.005555555555555556));
	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 = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / 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((-0.5 * (B / (C - A)))) / (pi * 0.005555555555555556);
	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[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $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 26.0

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

   2. Simplified 7.8

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

   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 50.5

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

   2. Simplified 49.4

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

   3. Applied egg-rr 55.0

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

   4. Taylor expanded in B around 0 1.6

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C - A}\right)}}{\pi \cdot 0.005555555555555556} \]
3. Recombined 2 regimes into one program.

4. Final simplification 7.0

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

Alternatives

Alternative 1
Error	11.9
Cost	20164

\[\begin{array}{l} \mathbf{if}\;A \leq -9.964066889392312 \cdot 10^{-43}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(C - A, B\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2
Error	13.9
Cost	20104

\[\begin{array}{l} \mathbf{if}\;A \leq -9.964066889392312 \cdot 10^{-43}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.743861327797474 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \end{array} \]

Alternative 3
Error	15.5
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -9.964066889392312 \cdot 10^{-43}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1665903.9731601197:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 4
Error	22.1
Cost	14748

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(-1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + t_1\right)\\ \mathbf{elif}\;B \leq 1.3723459246350136 \cdot 10^{-278}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.178477089505927 \cdot 10^{-240}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \left(1 + \frac{C \cdot -0.5}{B}\right) \cdot \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.7979738531407206 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.3103607741160962 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.24007119742573 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.377382405278174 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\frac{-0.5}{B} \cdot \left(A \cdot A\right) - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	26.6
Cost	14496

\[\begin{array}{l} t_0 := \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ t_1 := \frac{180 \cdot t_0}{\pi}\\ t_2 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;C \leq -2.76312199182845 \cdot 10^{+58}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;C \leq 1.56412464788566 \cdot 10^{-192}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;C \leq 3.8218487431218866 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.2494719204683536 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 2.202872230310033 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2.680009139261294 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 7.429472139374331 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 1.1413674923770725 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	25.0
Cost	14364

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq 1.56412464788566 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 3.8218487431218866 \cdot 10^{-182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.2494719204683536 \cdot 10^{-141}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.202872230310033 \cdot 10^{-108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.680009139261294 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 7.429472139374331 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 1.1413674923770725 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	21.7
Cost	14220

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + t_1\right)\\ \mathbf{elif}\;B \leq 1.3723459246350136 \cdot 10^{-278}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.178477089505927 \cdot 10^{-240}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \left(1 + \frac{C \cdot -0.5}{B}\right) \cdot \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.7979738531407206 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + t_1\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	29.3
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -4.819519392148164 \cdot 10^{-127}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{elif}\;A \leq -2.6893162964263513 \cdot 10^{-307}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.506365570838248 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.741765788604371 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 94.66549211853265:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	29.3
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -4.819519392148164 \cdot 10^{-127}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{elif}\;A \leq -2.6893162964263513 \cdot 10^{-307}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.506365570838248 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.741765788604371 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 94.66549211853265:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 10
Error	21.8
Cost	13968

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + t_1\right)\\ \mathbf{elif}\;B \leq 1.3723459246350136 \cdot 10^{-278}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.178477089505927 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7979738531407206 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + t_1\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	29.5
Cost	13840

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.3624841089329168 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -0.024239983720374995:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.4816193572504494 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	26.3
Cost	13840

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;A \leq -1.158876486019641 \cdot 10^{-126}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{elif}\;A \leq 7.741765788604371 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.7420839073705013 \cdot 10^{-63}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 1.743861327797474 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 13
Error	26.2
Cost	13840

\[\begin{array}{l} t_0 := \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;A \leq -1.158876486019641 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.741765788604371 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.7420839073705013 \cdot 10^{-63}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 1.743861327797474 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 14
Error	31.8
Cost	13708

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.3624841089329168 \cdot 10^{+66}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.4816193572504494 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 15
Error	35.3
Cost	13320

\[\begin{array}{l} \mathbf{if}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 6.24007119742573 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	45.8
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -4.9162511484124144 \cdot 10^{-219}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \]

Alternative 17
Error	55.1
Cost	13056

\[180 \cdot \frac{\tan^{-1} 0}{\pi} \]

Reproduce

herbie shell --seed 2022225 
(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)))