ABCF->ab-angle angle

Average Error: 30.2 → 11.7

Time: 23.2s

Precision: binary64

Cost: 60489

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-50} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \end{array} \]

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 -1e-50) (not (<= t_0 0.0)))
     (* (atan (/ (- (- C A) (hypot B (- A C))) B)) (/ 180.0 PI))
     (* (/ 180.0 PI) (atan (/ (* B 0.5) A))))))

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 <= -1e-50) || !(t_0 <= 0.0)) {
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	}
	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 <= -1e-50) || !(t_0 <= 0.0)) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	}
	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 <= -1e-50) or not (t_0 <= 0.0):
		tmp = math.atan((((C - A) - math.hypot(B, (A - C))) / B)) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	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 <= -1e-50) || !(t_0 <= 0.0))
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	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 <= -1e-50) || ~((t_0 <= 0.0)))
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	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, -1e-50], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $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))))) < -1.00000000000000001e-50 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 26.8

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

   2. Simplified 8.5

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

      [Start] 26.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 26.8	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 26.8	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 26.8	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 26.7	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 26.7	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 26.7	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 26.7	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 26.7	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 8.5	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   if -1.00000000000000001e-50 < (*.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 52.5

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

   2. Simplified 56.4

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

      [Start] 52.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 52.5	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 52.5	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 52.5	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Taylor expanded in A around -inf 31.8

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

   4. Simplified 31.8

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

      [Start] 31.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \]
      associate-*r/ [=>] 31.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)} \]
      *-commutative [=>] 31.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{B \cdot 0.5}}{A}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 11.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -1 \cdot 10^{-50} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	18.9
Cost	20296

\[\begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+116}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A \cdot A}{C}}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \left(C - \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	29.3
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 4.9 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.95 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-\frac{A}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 3
Error	27.9
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -4.4 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 4
Error	28.0
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -4.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 8.2 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.06 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 5
Error	28.0
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_2 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -4.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{t_2}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_2\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-224}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 6
Error	27.9
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_2 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_3 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{t_2}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_2\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 7
Error	28.0
Cost	14500

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -4.3 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{-180}{\frac{-\pi}{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 6.6 \cdot 10^{-72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 8
Error	33.7
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-\frac{A}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9
Error	33.9
Cost	14104

\[\begin{array}{l} t_0 := \frac{\frac{\tan^{-1} \left(-\frac{A}{B}\right)}{0.005555555555555556}}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -9 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-190}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-180}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10
Error	31.6
Cost	13840

\[\begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-262}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Error	31.6
Cost	13840

\[\begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-263}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-178}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	25.0
Cost	13840

\[\begin{array}{l} \mathbf{if}\;B \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 13
Error	22.0
Cost	13572

\[\begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-191}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 14
Error	34.7
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15
Error	38.2
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-301}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16
Error	51.0
Cost	13056

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

Reproduce

herbie shell --seed 2023018 
(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)))