ABCF->ab-angle angle

Average Error: 29.5 → 26.5

Time: 17.1s

Precision: binary64

Cost: 33360

Math

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

↓

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ t_1 := 1 + \frac{C}{B}\\ \mathbf{if}\;A \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{{A}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t_1}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-286}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

FPCore

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

↓

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))) (t_1 (+ 1.0 (/ C B))))
   (if (<= A -1.15e-18)
     (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (/ (* B C) (pow A 2.0))))) PI))
     (if (<= A -3.5e-263)
       (* 180.0 (/ (atan t_1) PI))
       (if (<= A 2e-286)
         t_0
         (if (<= A 9.2e-200)
           (*
            180.0
            (/ (atan (- (/ (+ A (sqrt (+ (pow B 2.0) (pow A 2.0)))) B))) PI))
           (if (<= A 5e-173)
             t_0
             (if (<= A 2.05e-38)
               (* 180.0 (/ (atan (- t_1 (/ A B))) PI))
               (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))))))

C

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

↓

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	double t_1 = 1.0 + (C / B);
	double tmp;
	if (A <= -1.15e-18) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B * C) / pow(A, 2.0))))) / ((double) M_PI));
	} else if (A <= -3.5e-263) {
		tmp = 180.0 * (atan(t_1) / ((double) M_PI));
	} else if (A <= 2e-286) {
		tmp = t_0;
	} else if (A <= 9.2e-200) {
		tmp = 180.0 * (atan(-((A + sqrt((pow(B, 2.0) + pow(A, 2.0)))) / B)) / ((double) M_PI));
	} else if (A <= 5e-173) {
		tmp = t_0;
	} else if (A <= 2.05e-38) {
		tmp = 180.0 * (atan((t_1 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

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

↓

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	double t_1 = 1.0 + (C / B);
	double tmp;
	if (A <= -1.15e-18) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B * C) / Math.pow(A, 2.0))))) / Math.PI);
	} else if (A <= -3.5e-263) {
		tmp = 180.0 * (Math.atan(t_1) / Math.PI);
	} else if (A <= 2e-286) {
		tmp = t_0;
	} else if (A <= 9.2e-200) {
		tmp = 180.0 * (Math.atan(-((A + Math.sqrt((Math.pow(B, 2.0) + Math.pow(A, 2.0)))) / B)) / Math.PI);
	} else if (A <= 5e-173) {
		tmp = t_0;
	} else if (A <= 2.05e-38) {
		tmp = 180.0 * (Math.atan((t_1 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

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

↓

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	t_1 = 1.0 + (C / B)
	tmp = 0
	if A <= -1.15e-18:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B * C) / math.pow(A, 2.0))))) / math.pi)
	elif A <= -3.5e-263:
		tmp = 180.0 * (math.atan(t_1) / math.pi)
	elif A <= 2e-286:
		tmp = t_0
	elif A <= 9.2e-200:
		tmp = 180.0 * (math.atan(-((A + math.sqrt((math.pow(B, 2.0) + math.pow(A, 2.0)))) / B)) / math.pi)
	elif A <= 5e-173:
		tmp = t_0
	elif A <= 2.05e-38:
		tmp = 180.0 * (math.atan((t_1 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

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

↓

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi))
	t_1 = Float64(1.0 + Float64(C / B))
	tmp = 0.0
	if (A <= -1.15e-18)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B * C) / (A ^ 2.0))))) / pi));
	elseif (A <= -3.5e-263)
		tmp = Float64(180.0 * Float64(atan(t_1) / pi));
	elseif (A <= 2e-286)
		tmp = t_0;
	elseif (A <= 9.2e-200)
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(Float64(A + sqrt(Float64((B ^ 2.0) + (A ^ 2.0)))) / B))) / pi));
	elseif (A <= 5e-173)
		tmp = t_0;
	elseif (A <= 2.05e-38)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) - 1.0)) / pi);
	t_1 = 1.0 + (C / B);
	tmp = 0.0;
	if (A <= -1.15e-18)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B * C) / (A ^ 2.0))))) / pi);
	elseif (A <= -3.5e-263)
		tmp = 180.0 * (atan(t_1) / pi);
	elseif (A <= 2e-286)
		tmp = t_0;
	elseif (A <= 9.2e-200)
		tmp = 180.0 * (atan(-((A + sqrt(((B ^ 2.0) + (A ^ 2.0)))) / B)) / pi);
	elseif (A <= 5e-173)
		tmp = t_0;
	elseif (A <= 2.05e-38)
		tmp = 180.0 * (atan((t_1 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.15e-18], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B * C), $MachinePrecision] / N[Power[A, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.5e-263], N[(180.0 * N[(N[ArcTan[t$95$1], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-286], t$95$0, If[LessEqual[A, 9.2e-200], N[(180.0 * N[(N[ArcTan[(-N[(N[(A + N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[A, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e-173], t$95$0, If[LessEqual[A, 2.05e-38], N[(180.0 * N[(N[ArcTan[N[(t$95$1 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -1.15e-18

   1. Initial program 47.7

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

   2. Taylor expanded in A around -inf 24.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   3. Simplified 24.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{{A}^{2}}\right)\right)}}{\pi} \]
      Proof

      [Start] 24.5	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 24.5	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A} + 0.5 \cdot \frac{C \cdot B}{{A}^{2}}\right)}}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 24.5	\[ 180 \cdot \frac{\tan^{-1} \left(\color{blue}{\frac{B}{A} \cdot 0.5} + 0.5 \cdot \frac{C \cdot B}{{A}^{2}}\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-23 [=>] 24.5	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{B}{A} + \frac{C \cdot B}{{A}^{2}}\right)\right)}}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 24.5	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{\color{blue}{B \cdot C}}{{A}^{2}}\right)\right)}{\pi} \]

   if -1.15e-18 < A < -3.49999999999999969e-263

   1. Initial program 29.9

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

   2. Taylor expanded in B around -inf 33.7

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

   3. Taylor expanded in A around 0 33.6

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

   if -3.49999999999999969e-263 < A < 2.0000000000000001e-286 or 9.2000000000000003e-200 < A < 5.0000000000000002e-173

   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. Taylor expanded in B around inf 31.4

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

   3. Taylor expanded in A around 0 32.1

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

   if 2.0000000000000001e-286 < A < 9.2000000000000003e-200

   1. Initial program 28.6

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

   2. Taylor expanded in C around 0 40.5

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

   3. Simplified 40.5

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

      [Start] 40.5	\[ 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 40.5	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B} \cdot -1\right)}}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 40.5	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}}{\pi} \]

   if 5.0000000000000002e-173 < A < 2.0499999999999999e-38

   1. Initial program 23.4

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

   2. Taylor expanded in B around -inf 29.6

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

   if 2.0499999999999999e-38 < A

   1. Initial program 16.6

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

   2. Taylor expanded in B around inf 16.7

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

   3. Taylor expanded in C around 0 16.9

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

   4. Simplified 16.9

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

      [Start] 16.9	\[ 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \left(1 + \frac{A}{B}\right)\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 16.9	\[ 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{\left(\frac{A}{B} + 1\right)}\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-1 [<=] 16.9	\[ 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{\left(\frac{A}{B} - -1\right)}\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-87 [=>] 16.9	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(--1\right) \cdot \left(-1 - \frac{A}{B}\right)\right)}}{\pi} \]
      metadata-eval [=>] 16.9	\[ 180 \cdot \frac{\tan^{-1} \left(\color{blue}{1} \cdot \left(-1 - \frac{A}{B}\right)\right)}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 16.9	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1 - \frac{A}{B}\right) \cdot 1\right)}}{\pi} \]
      rational_best_oopsla_all_46_json_45_simplify-52 [=>] 16.9	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

3. Recombined 6 regimes into one program.

4. Final simplification 26.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{{A}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-286}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	24.1
Cost	33548

\[\begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{{A}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{+81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	25.8
Cost	20292

\[\begin{array}{l} t_0 := 1 + \frac{C}{B}\\ \mathbf{if}\;A \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{{A}^{2}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t_0}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	25.5
Cost	14096

\[\begin{array}{l} t_0 := 1 + \frac{C}{B}\\ \mathbf{if}\;A \leq -2.05 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t_0}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4
Error	33.7
Cost	13840

\[\begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-112}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.6 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.4 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Error	28.7
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-262}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6
Error	26.5
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.6 \cdot 10^{-266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	33.7
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	25.6
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	34.3
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10
Error	38.4
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	50.5
Cost	13056

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

Reproduce

herbie shell --seed 2023090 
(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)))