ABCF->ab-angle angle

Percentage Accurate: 53.2% → 82.1%

Time: 18.6s

Precision: binary64

Cost: 60489

Math

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

↓

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

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)))
     (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) (* PI 0.005555555555555556))
     (/ (atan (* -0.5 (/ B C))) (* PI 0.005555555555555556)))))

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 = atan((((C - A) - hypot(B, (A - C))) / B)) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = atan((-0.5 * (B / C))) / (((double) M_PI) * 0.005555555555555556);
	}
	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 = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = Math.atan((-0.5 * (B / C))) / (Math.PI * 0.005555555555555556);
	}
	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 = math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / (math.pi * 0.005555555555555556)
	else:
		tmp = math.atan((-0.5 * (B / C))) / (math.pi * 0.005555555555555556)
	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(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B / C))) / Float64(pi * 0.005555555555555556));
	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 = atan((((C - A) - hypot(B, (A - C))) / B)) / (pi * 0.005555555555555556);
	else
		tmp = atan((-0.5 * (B / C))) / (pi * 0.005555555555555556);
	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[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $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))))) < -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 59.6%

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

   2. Simplified 88.4%

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

      [Start] 59.6%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 59.7%	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 59.7%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 59.7%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 59.7%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 59.7%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 88.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Applied egg-rr 82.6%

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

      [Start] 88.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \]
      associate-*r/ [=>] 88.4%	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      associate--r+ [<=] 82.6%	\[ \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\pi} \]
      associate-*l/ [<=] 82.6%	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      *-commutative [=>] 82.6%	\[ \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
      associate--r+ [=>] 88.4%	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]
      clear-num [=>] 88.4%	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \color{blue}{\frac{1}{\frac{\pi}{180}}} \]
      un-div-inv [=>] 88.4%	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\frac{\pi}{180}}} \]
      associate--r+ [<=] 82.6%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 82.6%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]
      metadata-eval [=>] 82.6%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   4. Simplified 88.4%

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

      [Start] 82.6%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--r+ [=>] 88.4%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   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 16.3%

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

   2. Simplified 16.3%

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

      [Start] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Applied egg-rr 4.4%

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

      [Start] 16.3%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \]
      associate-*r/ [=>] 16.3%	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      associate--r+ [<=] 4.4%	\[ \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\pi} \]
      associate-*l/ [<=] 4.4%	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      *-commutative [=>] 4.4%	\[ \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
      associate--r+ [=>] 16.3%	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]
      clear-num [=>] 16.3%	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \color{blue}{\frac{1}{\frac{\pi}{180}}} \]
      un-div-inv [=>] 16.3%	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\frac{\pi}{180}}} \]
      associate--r+ [<=] 4.4%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 4.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]
      metadata-eval [=>] 4.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   4. Simplified 16.3%

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

      [Start] 4.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--r+ [=>] 16.3%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   5. Taylor expanded in C around inf 30.4%

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

   6. Simplified 38.5%

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, 0\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      Step-by-step derivation

      [Start] 30.4%	\[ \frac{\tan^{-1} \left(\frac{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      fma-def [=>] 30.4%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--l+ [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      fma-def [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      difference-of-squares [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      distribute-rgt1-in [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul0-lft [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul-1-neg [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      distribute-rgt1-in [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul0-lft [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 38.5%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   7. Taylor expanded in B around 0 60.7%

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

4. Final simplification 84.7%

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

Alternatives

Alternative 1
Accuracy	82.1%
Cost	60489

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

Alternative 2
Accuracy	80.3%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3
Accuracy	77.0%
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -5.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 7.8 \cdot 10^{+46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 4
Accuracy	77.0%
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -3.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 5
Accuracy	77.7%
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -1.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 6
Accuracy	73.8%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -9.2 \cdot 10^{+164}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 7
Accuracy	73.8%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+192}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 8
Accuracy	73.8%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+164}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{+192}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 9
Accuracy	56.2%
Cost	14104

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{if}\;A \leq -5.1 \cdot 10^{+98}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.6 \cdot 10^{-202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 0.35:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10
Accuracy	44.8%
Cost	13976

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -115:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11
Accuracy	54.7%
Cost	13972

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.5 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-286}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 0.35:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12
Accuracy	62.9%
Cost	13969

\[\begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-212}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;B \leq 1.36 \cdot 10^{-50} \lor \neg \left(B \leq 2.15 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 13
Accuracy	62.9%
Cost	13969

\[\begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-50} \lor \neg \left(B \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 14
Accuracy	62.6%
Cost	13969

\[\begin{array}{l} \mathbf{if}\;B \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;B \leq 1.36 \cdot 10^{-50} \lor \neg \left(B \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 15
Accuracy	48.1%
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -5.8 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16
Accuracy	53.4%
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -6.3 \cdot 10^{+91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-286}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.52 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17
Accuracy	57.5%
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.65 \cdot 10^{+97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-286}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.32 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18
Accuracy	58.8%
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 19
Accuracy	47.9%
Cost	13776

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20
Accuracy	45.2%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21
Accuracy	40.2%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq 7 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22
Accuracy	21.0%
Cost	13056

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

Reproduce

herbie shell --seed 2023165 
(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)))