ABCF->ab-angle angle

Average Error: 29.8 → 10.9

Time: 18.4s

Precision: binary64

Cost: 60488

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_1}{0.005555555555555556}}{\pi}\\ \end{array} \]

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))))))
        (t_1 (atan (/ (- (- C A) (hypot B (- A C))) B))))
   (if (<= t_0 -5e-113)
     (* 180.0 (/ t_1 PI))
     (if (<= t_0 0.0)
       (/ (atan (* 0.5 (/ B A))) (/ PI 180.0))
       (/ (/ t_1 0.005555555555555556) 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 t_1 = atan((((C - A) - hypot(B, (A - C))) / B));
	double tmp;
	if (t_0 <= -5e-113) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = atan((0.5 * (B / A))) / (((double) M_PI) / 180.0);
	} else {
		tmp = (t_1 / 0.005555555555555556) / ((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 t_1 = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B));
	double tmp;
	if (t_0 <= -5e-113) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = Math.atan((0.5 * (B / A))) / (Math.PI / 180.0);
	} else {
		tmp = (t_1 / 0.005555555555555556) / 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))))
	t_1 = math.atan((((C - A) - math.hypot(B, (A - C))) / B))
	tmp = 0
	if t_0 <= -5e-113:
		tmp = 180.0 * (t_1 / math.pi)
	elif t_0 <= 0.0:
		tmp = math.atan((0.5 * (B / A))) / (math.pi / 180.0)
	else:
		tmp = (t_1 / 0.005555555555555556) / 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)))))
	t_1 = atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))
	tmp = 0.0
	if (t_0 <= -5e-113)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) / Float64(pi / 180.0));
	else
		tmp = Float64(Float64(t_1 / 0.005555555555555556) / 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))));
	t_1 = atan((((C - A) - hypot(B, (A - C))) / B));
	tmp = 0.0;
	if (t_0 <= -5e-113)
		tmp = 180.0 * (t_1 / pi);
	elseif (t_0 <= 0.0)
		tmp = atan((0.5 * (B / A))) / (pi / 180.0);
	else
		tmp = (t_1 / 0.005555555555555556) / 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]}, Block[{t$95$1 = N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -5e-113], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 / 0.005555555555555556), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.9999999999999997e-113

   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 8.1

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

      [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-*l/ [=>] 26.8	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 26.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 26.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 26.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 26.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 8.1	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   if -4.9999999999999997e-113 < (*.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 52.6

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

   2. Simplified 56.5

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

      [Start] 52.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 52.6	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 52.6	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 52.6	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 52.6

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

   4. Taylor expanded in A around -inf 37.9

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{{B}^{2}}{A}}}{B}\right)}{0.005555555555555556}}{\pi} \]

   5. Simplified 37.9

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{\frac{B \cdot \left(B \cdot 0.5\right)}{A}}}{B}\right)}{0.005555555555555556}}{\pi} \]
      Proof

      [Start] 37.9	\[ \frac{\frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}{0.005555555555555556}}{\pi} \]
      associate-*r/ [=>] 37.9	\[ \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{\frac{0.5 \cdot {B}^{2}}{A}}}{B}\right)}{0.005555555555555556}}{\pi} \]
      *-commutative [=>] 37.9	\[ \frac{\frac{\tan^{-1} \left(\frac{\frac{\color{blue}{{B}^{2} \cdot 0.5}}{A}}{B}\right)}{0.005555555555555556}}{\pi} \]
      unpow2 [=>] 37.9	\[ \frac{\frac{\tan^{-1} \left(\frac{\frac{\color{blue}{\left(B \cdot B\right)} \cdot 0.5}{A}}{B}\right)}{0.005555555555555556}}{\pi} \]
      associate-*l* [=>] 37.9	\[ \frac{\frac{\tan^{-1} \left(\frac{\frac{\color{blue}{B \cdot \left(B \cdot 0.5\right)}}{A}}{B}\right)}{0.005555555555555556}}{\pi} \]

   6. Taylor expanded in B around 0 30.6

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

   7. Simplified 30.5

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

      [Start] 30.6	\[ 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \]
      associate-*r/ [=>] 30.6	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]
      *-commutative [<=] 30.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{B \cdot 0.5}}{A}\right)}{\pi} \]
      /-rgt-identity [<=] 30.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\frac{B}{1}} \cdot 0.5}{A}\right)}{\pi} \]
      *-inverses [<=] 30.6	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\frac{B}{\color{blue}{\frac{B}{B}}} \cdot 0.5}{A}\right)}{\pi} \]
      associate-/l* [<=] 35.5	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\frac{B \cdot B}{B}} \cdot 0.5}{A}\right)}{\pi} \]
      associate-*r/ [<=] 35.6	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{B \cdot B}{B} \cdot \frac{0.5}{A}\right)}}{\pi} \]
      associate-*r/ [=>] 35.6	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot B}{B} \cdot \frac{0.5}{A}\right)}{\pi}} \]
      *-commutative [<=] 35.6	\[ \frac{\color{blue}{\tan^{-1} \left(\frac{B \cdot B}{B} \cdot \frac{0.5}{A}\right) \cdot 180}}{\pi} \]
      associate-/l* [=>] 35.5	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot B}{B} \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}} \]
      associate-*r/ [=>] 35.5	\[ \frac{\tan^{-1} \color{blue}{\left(\frac{\frac{B \cdot B}{B} \cdot 0.5}{A}\right)}}{\frac{\pi}{180}} \]
      associate-/l* [=>] 30.5	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\frac{B}{\frac{B}{B}}} \cdot 0.5}{A}\right)}{\frac{\pi}{180}} \]
      *-inverses [=>] 30.5	\[ \frac{\tan^{-1} \left(\frac{\frac{B}{\color{blue}{1}} \cdot 0.5}{A}\right)}{\frac{\pi}{180}} \]
      /-rgt-identity [=>] 30.5	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{B} \cdot 0.5}{A}\right)}{\frac{\pi}{180}} \]
      *-commutative [=>] 30.5	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot B}}{A}\right)}{\frac{\pi}{180}} \]
      associate-*r/ [<=] 30.5	\[ \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\frac{\pi}{180}} \]

   if -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 10.6

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

      [Start] 26.0	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 26.0	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 26.0	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 26.0	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 8.0

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

4. Final simplification 10.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Error	25.3
Cost	20496

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + \left(C - A\right)}{B}\right)\\ \mathbf{if}\;C \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-297}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 7.3 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 2
Error	13.1
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 3
Error	13.1
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 6 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{0.005555555555555556}}{\pi}\\ \end{array} \]

Alternative 4
Error	34.2
Cost	14236

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.65 \cdot 10^{-255}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Error	25.4
Cost	13968

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + \left(C - A\right)}{B}\right)\\ \mathbf{if}\;C \leq -2.25 \cdot 10^{-67}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 2 \cdot 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6
Error	27.9
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -2.25 \cdot 10^{-67}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 7
Error	28.0
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -2.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 8
Error	26.1
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -1.76 \cdot 10^{-71}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 9
Error	25.9
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -8.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;C \leq 1.2 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	25.7
Cost	13840

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -7 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.55 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 11
Error	33.9
Cost	13712

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -5.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12
Error	33.3
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -6.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-300}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 13
Error	35.1
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -2.25 \cdot 10^{-165}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14
Error	38.5
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-304}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15
Error	50.7
Cost	13056

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

Reproduce

herbie shell --seed 2023041 
(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)))