ABCF->ab-angle angle

Percentage Accurate: 53.9% → 81.5%

Time: 29.6s

Precision: binary64

Cost: 20164

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;C \leq 4.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

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
 (if (<= C 4.6e+107)
   (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) (* PI 0.005555555555555556))
   (/ (atan (/ B (/ C -0.5))) (* 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 tmp;
	if (C <= 4.6e+107) {
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = atan((B / (C / -0.5))) / (((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 tmp;
	if (C <= 4.6e+107) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = Math.atan((B / (C / -0.5))) / (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):
	tmp = 0
	if C <= 4.6e+107:
		tmp = math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / (math.pi * 0.005555555555555556)
	else:
		tmp = math.atan((B / (C / -0.5))) / (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)
	tmp = 0.0
	if (C <= 4.6e+107)
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / 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)
	tmp = 0.0;
	if (C <= 4.6e+107)
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) / (pi * 0.005555555555555556);
	else
		tmp = atan((B / (C / -0.5))) / (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_] := If[LessEqual[C, 4.6e+107], 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[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 4.6000000000000001e107

   1. Initial program 64.8%

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

   2. Simplified 82.8%

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

      [Start] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 64.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 82.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Applied egg-rr 77.5%

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

      [Start] 82.8%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \]
      associate-*r/ [=>] 82.8%	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      associate--r+ [<=] 77.4%	\[ \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\pi} \]
      associate-*l/ [<=] 77.4%	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      *-commutative [=>] 77.4%	\[ \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
      associate--r+ [=>] 82.8%	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]
      clear-num [=>] 82.8%	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \color{blue}{\frac{1}{\frac{\pi}{180}}} \]
      un-div-inv [=>] 82.8%	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\frac{\pi}{180}}} \]
      associate--r+ [<=] 77.5%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 77.5%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]
      metadata-eval [=>] 77.5%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   4. Simplified 82.8%

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

      [Start] 77.5%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--r+ [=>] 82.8%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   if 4.6000000000000001e107 < C

   1. Initial program 15.4%

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

   2. Simplified 42.4%

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

      [Start] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*l/ [=>] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]
      *-lft-identity [=>] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]
      +-commutative [=>] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]
      unpow2 [=>] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]
      unpow2 [=>] 15.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]
      hypot-def [=>] 42.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Applied egg-rr 42.4%

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

      [Start] 42.4%	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \]
      associate-*r/ [=>] 42.4%	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
      associate--r+ [<=] 42.4%	\[ \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\pi} \]
      associate-*l/ [<=] 42.4%	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      *-commutative [=>] 42.4%	\[ \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
      associate--r+ [=>] 42.4%	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]
      clear-num [=>] 42.4%	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \color{blue}{\frac{1}{\frac{\pi}{180}}} \]
      un-div-inv [=>] 42.4%	\[ \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\frac{\pi}{180}}} \]
      associate--r+ [<=] 42.4%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}{B}\right)}{\frac{\pi}{180}} \]
      div-inv [=>] 42.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\color{blue}{\pi \cdot \frac{1}{180}}} \]
      metadata-eval [=>] 42.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   4. Simplified 42.4%

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

      [Start] 42.4%	\[ \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--r+ [=>] 42.4%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   5. Taylor expanded in C around inf 55.5%

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

   6. Simplified 67.4%

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

      [Start] 55.5%	\[ \frac{\tan^{-1} \left(\frac{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      fma-def [=>] 55.5%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      associate--l+ [=>] 59.7%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 59.7%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      fma-def [=>] 59.7%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 59.7%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      unpow2 [=>] 59.7%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      difference-of-squares [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      distribute-rgt1-in [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul0-lft [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul-1-neg [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      distribute-rgt1-in [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      mul0-lft [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]
      metadata-eval [=>] 67.4%	\[ \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi \cdot 0.005555555555555556} \]

   7. Taylor expanded in B around 0 89.7%

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

   8. Simplified 89.7%

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

      [Start] 89.7%	\[ \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot 0.005555555555555556} \]
      associate-*r/ [=>] 89.7%	\[ \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi \cdot 0.005555555555555556} \]
      *-commutative [=>] 89.7%	\[ \frac{\tan^{-1} \left(\frac{\color{blue}{B \cdot -0.5}}{C}\right)}{\pi \cdot 0.005555555555555556} \]
      associate-/l* [=>] 89.7%	\[ \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C}{-0.5}}\right)}}{\pi \cdot 0.005555555555555556} \]

3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 4.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.5%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 4.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2
Accuracy	81.5%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3
Accuracy	78.5%
Cost	20104

\[\begin{array}{l} \mathbf{if}\;C \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 4
Accuracy	75.0%
Cost	20040

\[\begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{+38}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	46.4%
Cost	14040

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.3 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.05 \cdot 10^{-304}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Accuracy	46.1%
Cost	13712

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Accuracy	52.0%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-232}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8
Accuracy	52.0%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9
Accuracy	56.4%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -3.7 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -9 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 10
Accuracy	56.4%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -3.7 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.15 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.06 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 11
Accuracy	56.4%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;C \leq -3.7 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.95 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 12
Accuracy	61.1%
Cost	13704

\[\begin{array}{l} \mathbf{if}\;C \leq -50:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 13
Accuracy	61.1%
Cost	13704

\[\begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.16 \cdot 10^{-95}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 14
Accuracy	61.2%
Cost	13704

\[\begin{array}{l} \mathbf{if}\;C \leq -2 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 15
Accuracy	47.7%
Cost	13644

\[\begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.5 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 10^{-151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16
Accuracy	61.1%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;C \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.04 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 17
Accuracy	44.7%
Cost	13448

\[\begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Accuracy	40.3%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19
Accuracy	20.9%
Cost	13056

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

Reproduce

herbie shell --seed 2023263 
(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)))