ABCF->ab-angle angle

Percentage Accurate: 53.7% → 81.4%

Time: 24.4s

Alternatives: 20

Speedup: 3.2×

Specification

Math

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

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)))

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));
}

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);
}

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)

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

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

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]

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

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)))

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));
}

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);
}

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)

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

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

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]

Alternative 1: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+126}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.8e+126)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+126) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+126) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.8e+126:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.8e+126)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.8e+126)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.8e+126], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.80000000000000024e126

   1. Initial program 16.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 16.8%

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

      2. associate-*l/ 16.8%

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

      3. *-un-lft-identity 16.8%

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

      4. unpow2 16.8%

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

      5. unpow2 16.8%

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

      6. hypot-define 47.1%

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

   4. Applied egg-rr 47.1%

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

   5. Taylor expanded in A around -inf 79.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 79.0%

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

      2. associate-/l* 79.3%

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

   7. Applied egg-rr 79.3%

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

   if -4.80000000000000024e126 < A

   1. Initial program 60.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 60.2%

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

      2. associate-*l/ 60.2%

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

      3. *-un-lft-identity 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-define 84.5%

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

   4. Applied egg-rr 84.5%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+126}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.05 \cdot 10^{+107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right) \cdot -180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.05e+107)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= C 5.2e+125)
     (/ (* (atan (/ (+ A (hypot B A)) B)) -180.0) PI)
     (/ (atan (/ (* B -0.5) C)) (* PI 0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.05e+107) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (C <= 5.2e+125) {
		tmp = (atan(((A + hypot(B, A)) / B)) * -180.0) / ((double) M_PI);
	} else {
		tmp = atan(((B * -0.5) / C)) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.05e+107) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (C <= 5.2e+125) {
		tmp = (Math.atan(((A + Math.hypot(B, A)) / B)) * -180.0) / Math.PI;
	} else {
		tmp = Math.atan(((B * -0.5) / C)) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.05e+107:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif C <= 5.2e+125:
		tmp = (math.atan(((A + math.hypot(B, A)) / B)) * -180.0) / math.pi
	else:
		tmp = math.atan(((B * -0.5) / C)) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.05e+107)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (C <= 5.2e+125)
		tmp = Float64(Float64(atan(Float64(Float64(A + hypot(B, A)) / B)) * -180.0) / pi);
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / C)) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.05e+107)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (C <= 5.2e+125)
		tmp = (atan(((A + hypot(B, A)) / B)) * -180.0) / pi;
	else
		tmp = atan(((B * -0.5) / C)) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.05e+107], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.2e+125], N[(N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * -180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.05e107

   1. Initial program 80.3%

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

   3. Taylor expanded in B around -inf 82.1%

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

      1. associate--l+ 82.1%

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

      2. div-sub 84.4%

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

   5. Simplified 84.4%

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

   if -1.05e107 < C < 5.20000000000000006e125

   1. Initial program 54.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 54.3%

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

      2. associate-*l/ 54.3%

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

      3. *-un-lft-identity 54.3%

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

      4. unpow2 54.3%

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

      5. unpow2 54.3%

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

      6. hypot-define 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in C around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-neg-frac2 49.9%

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

      3. unpow2 49.9%

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

      4. unpow2 49.9%

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

      5. hypot-define 77.1%

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

   7. Simplified 77.1%

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

      1. distribute-frac-neg2 77.1%

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

      2. atan-neg 77.1%

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

      3. add-sqr-sqrt 37.2%

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

      4. sqrt-unprod 23.4%

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

      5. sqr-neg 23.4%

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

      6. sqrt-unprod 4.7%

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

      7. add-sqr-sqrt 9.2%

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

      8. distribute-rgt-neg-in 9.2%

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

      9. neg-sub0 9.2%

         \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}}{\pi} \]

      10. add-sqr-sqrt 4.7%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{-B} \cdot \sqrt{-B}}}\right)}{\pi} \]

      11. sqrt-unprod 23.4%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{\left(-B\right) \cdot \left(-B\right)}}}\right)}{\pi} \]

      12. sqr-neg 23.4%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\sqrt{\color{blue}{B \cdot B}}}\right)}{\pi} \]

      13. sqrt-unprod 37.2%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}\right)}{\pi} \]

      14. add-sqr-sqrt 77.1%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{B}}\right)}{\pi} \]

   9. Applied egg-rr 77.1%

      \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. neg-sub0 77.1%

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

       2. *-commutative 77.1%

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

       3. distribute-rgt-neg-in 77.1%

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

       4. *-lft-identity 77.1%

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

       5. *-lft-identity 77.1%

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

       6. hypot-undefine 49.9%

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

       7. unpow2 49.9%

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

       8. unpow2 49.9%

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

       9. +-commutative 49.9%

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

       10. unpow2 49.9%

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

       11. unpow2 49.9%

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

       12. hypot-define 77.1%

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

       13. metadata-eval 77.1%

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

   11. Simplified 77.1%

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

   if 5.20000000000000006e125 < C

   1. Initial program 15.0%

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

   3. Taylor expanded in C around inf 82.9%

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

   4. Taylor expanded in A around inf 82.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. *-commutative 82.9%

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

      2. associate-*l/ 83.1%

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

      3. +-rgt-identity 83.1%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C} + 0\right)} \cdot 180}{\pi} \]

      4. fma-define 83.1%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)} \cdot 180}{\pi} \]

      5. mul0-lft 78.0%

         \[\leadsto \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \color{blue}{0 \cdot \frac{A}{B}}\right)\right) \cdot 180}{\pi} \]

      6. associate-/l* 78.0%

         \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0 \cdot \frac{A}{B}\right)\right) \cdot \frac{180}{\pi}} \]

   6. Simplified 83.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
   7. Step-by-step derivation

      1. clear-num 83.0%

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

      2. un-div-inv 83.0%

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

      3. associate-*r/ 83.1%

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

      4. div-inv 83.1%

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

      5. metadata-eval 83.1%

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

   8. Applied egg-rr 83.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.05 \cdot 10^{+107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right) \cdot -180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+102}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.5e+102)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.5e+102) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.5e+102) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.5e+102:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.5e+102)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.5e+102)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.5e+102], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.50000000000000011e102

   1. Initial program 21.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 21.8%

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

      2. associate-*l/ 21.8%

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

      3. *-un-lft-identity 21.8%

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

      4. unpow2 21.8%

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

      5. unpow2 21.8%

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

      6. hypot-define 50.7%

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

   4. Applied egg-rr 50.7%

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

   5. Taylor expanded in A around -inf 77.6%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 77.6%

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

      2. associate-/l* 77.8%

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

   7. Applied egg-rr 77.8%

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

   if -3.50000000000000011e102 < A

   1. Initial program 60.1%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+102}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+125}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.1e+125)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e+125) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e+125) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.1e+125:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.1e+125)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.1e+125)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.1e+125], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.0999999999999998e125

   1. Initial program 16.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 16.8%

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

      2. associate-*l/ 16.8%

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

      3. *-un-lft-identity 16.8%

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

      4. unpow2 16.8%

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

      5. unpow2 16.8%

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

      6. hypot-define 47.1%

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

   4. Applied egg-rr 47.1%

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

   5. Taylor expanded in A around -inf 79.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 79.0%

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

      2. associate-/l* 79.3%

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

   7. Applied egg-rr 79.3%

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

   if -5.0999999999999998e125 < A

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-define 84.5%

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

   3. Simplified 84.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+125}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;C \leq -28500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq -6.8 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -2.9 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq -3.9 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-168}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 10^{-118}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI))
        (t_1 (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)))
   (if (<= C -28500000000.0)
     t_1
     (if (<= C -6.8e-74)
       t_0
       (if (<= C -2.9e-103)
         t_1
         (if (<= C -3.9e-140)
           (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
           (if (<= C 4e-168)
             t_0
             (if (<= C 1e-118)
               (/ (* -180.0 (atan (+ 1.0 (/ A B)))) PI)
               (if (<= C 1.9e+16)
                 t_0
                 (/
                  (atan (/ (* B -0.5) C))
                  (* PI 0.005555555555555556)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	double t_1 = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	double tmp;
	if (C <= -28500000000.0) {
		tmp = t_1;
	} else if (C <= -6.8e-74) {
		tmp = t_0;
	} else if (C <= -2.9e-103) {
		tmp = t_1;
	} else if (C <= -3.9e-140) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 4e-168) {
		tmp = t_0;
	} else if (C <= 1e-118) {
		tmp = (-180.0 * atan((1.0 + (A / B)))) / ((double) M_PI);
	} else if (C <= 1.9e+16) {
		tmp = t_0;
	} else {
		tmp = atan(((B * -0.5) / C)) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	double t_1 = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	double tmp;
	if (C <= -28500000000.0) {
		tmp = t_1;
	} else if (C <= -6.8e-74) {
		tmp = t_0;
	} else if (C <= -2.9e-103) {
		tmp = t_1;
	} else if (C <= -3.9e-140) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 4e-168) {
		tmp = t_0;
	} else if (C <= 1e-118) {
		tmp = (-180.0 * Math.atan((1.0 + (A / B)))) / Math.PI;
	} else if (C <= 1.9e+16) {
		tmp = t_0;
	} else {
		tmp = Math.atan(((B * -0.5) / C)) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	t_1 = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	tmp = 0
	if C <= -28500000000.0:
		tmp = t_1
	elif C <= -6.8e-74:
		tmp = t_0
	elif C <= -2.9e-103:
		tmp = t_1
	elif C <= -3.9e-140:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 4e-168:
		tmp = t_0
	elif C <= 1e-118:
		tmp = (-180.0 * math.atan((1.0 + (A / B)))) / math.pi
	elif C <= 1.9e+16:
		tmp = t_0
	else:
		tmp = math.atan(((B * -0.5) / C)) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi)
	t_1 = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi)
	tmp = 0.0
	if (C <= -28500000000.0)
		tmp = t_1;
	elseif (C <= -6.8e-74)
		tmp = t_0;
	elseif (C <= -2.9e-103)
		tmp = t_1;
	elseif (C <= -3.9e-140)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 4e-168)
		tmp = t_0;
	elseif (C <= 1e-118)
		tmp = Float64(Float64(-180.0 * atan(Float64(1.0 + Float64(A / B)))) / pi);
	elseif (C <= 1.9e+16)
		tmp = t_0;
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / C)) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((1.0 - (A / B)))) / pi;
	t_1 = (180.0 * atan(((C / B) + -1.0))) / pi;
	tmp = 0.0;
	if (C <= -28500000000.0)
		tmp = t_1;
	elseif (C <= -6.8e-74)
		tmp = t_0;
	elseif (C <= -2.9e-103)
		tmp = t_1;
	elseif (C <= -3.9e-140)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 4e-168)
		tmp = t_0;
	elseif (C <= 1e-118)
		tmp = (-180.0 * atan((1.0 + (A / B)))) / pi;
	elseif (C <= 1.9e+16)
		tmp = t_0;
	else
		tmp = atan(((B * -0.5) / C)) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -28500000000.0], t$95$1, If[LessEqual[C, -6.8e-74], t$95$0, If[LessEqual[C, -2.9e-103], t$95$1, If[LessEqual[C, -3.9e-140], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4e-168], t$95$0, If[LessEqual[C, 1e-118], N[(N[(-180.0 * N[ArcTan[N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 1.9e+16], t$95$0, N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -2.85e10 or -6.8000000000000001e-74 < C < -2.8999999999999999e-103

   1. Initial program 73.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 73.0%

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

      2. associate-*l/ 73.0%

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

      3. *-un-lft-identity 73.0%

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

      4. unpow2 73.0%

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

      5. unpow2 73.0%

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

      6. hypot-define 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in B around inf 77.4%

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

      1. +-commutative 77.4%

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

      2. associate--r+ 77.4%

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

      3. div-sub 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in C around inf 77.8%

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

   if -2.85e10 < C < -6.8000000000000001e-74 or -3.90000000000000019e-140 < C < 4.0000000000000002e-168 or 9.99999999999999985e-119 < C < 1.9e16

   1. Initial program 61.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 61.1%

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

      2. associate-*l/ 61.1%

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

      3. *-un-lft-identity 61.1%

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

      4. unpow2 61.1%

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

      5. unpow2 61.1%

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

      6. hypot-define 85.9%

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

   4. Applied egg-rr 85.9%

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

   5. Taylor expanded in C around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-neg-frac2 58.4%

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

      3. unpow2 58.4%

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

      4. unpow2 58.4%

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

      5. hypot-define 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in B around -inf 60.6%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. neg-mul-1 60.6%

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

      2. unsub-neg 60.6%

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

   10. Simplified 60.6%

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

   if -2.8999999999999999e-103 < C < -3.90000000000000019e-140

   1. Initial program 53.0%

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

   3. Taylor expanded in A around -inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 63.3%

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

   5. Simplified 63.3%

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

   if 4.0000000000000002e-168 < C < 9.99999999999999985e-119

   1. Initial program 50.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 50.5%

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

      2. associate-*l/ 50.5%

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

      3. *-un-lft-identity 50.5%

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

      4. unpow2 50.5%

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

      5. unpow2 50.5%

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

      6. hypot-define 76.5%

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

   4. Applied egg-rr 76.5%

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

   5. Taylor expanded in C around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-neg-frac2 50.5%

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

      3. unpow2 50.5%

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

      4. unpow2 50.5%

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

      5. hypot-define 76.7%

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

   7. Simplified 76.7%

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

      1. distribute-frac-neg2 76.7%

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

      2. atan-neg 76.7%

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

      3. add-sqr-sqrt 57.1%

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

      4. sqrt-unprod 27.8%

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

      5. sqr-neg 27.8%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.4%

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

      8. distribute-rgt-neg-in 2.4%

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

      9. neg-sub0 2.4%

         \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}}{\pi} \]

      10. add-sqr-sqrt 0.9%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{-B} \cdot \sqrt{-B}}}\right)}{\pi} \]

      11. sqrt-unprod 27.8%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{\left(-B\right) \cdot \left(-B\right)}}}\right)}{\pi} \]

      12. sqr-neg 27.8%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\sqrt{\color{blue}{B \cdot B}}}\right)}{\pi} \]

      13. sqrt-unprod 57.1%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}\right)}{\pi} \]

      14. add-sqr-sqrt 76.7%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{B}}\right)}{\pi} \]

   9. Applied egg-rr 76.7%

      \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. neg-sub0 76.7%

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

       2. *-commutative 76.7%

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

       3. distribute-rgt-neg-in 76.7%

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

       4. *-lft-identity 76.7%

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

       5. *-lft-identity 76.7%

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

       6. hypot-undefine 50.5%

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

       7. unpow2 50.5%

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

       8. unpow2 50.5%

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

       9. +-commutative 50.5%

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

       10. unpow2 50.5%

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

       11. unpow2 50.5%

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

       12. hypot-define 76.7%

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

       13. metadata-eval 76.7%

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

   11. Simplified 76.7%

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

   12. Taylor expanded in A around 0 70.0%

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

   if 1.9e16 < C

   1. Initial program 19.8%

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

   3. Taylor expanded in C around inf 68.1%

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

   4. Taylor expanded in A around inf 68.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

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

      2. associate-*l/ 68.2%

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

      3. +-rgt-identity 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C} + 0\right)} \cdot 180}{\pi} \]

      4. fma-define 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)} \cdot 180}{\pi} \]

      5. mul0-lft 65.0%

         \[\leadsto \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \color{blue}{0 \cdot \frac{A}{B}}\right)\right) \cdot 180}{\pi} \]

      6. associate-/l* 65.0%

         \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0 \cdot \frac{A}{B}\right)\right) \cdot \frac{180}{\pi}} \]

   6. Simplified 68.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
   7. Step-by-step derivation

      1. clear-num 68.1%

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

      2. un-div-inv 68.1%

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

      3. associate-*r/ 68.2%

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

      4. div-inv 68.2%

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

      5. metadata-eval 68.2%

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

   8. Applied egg-rr 68.2%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -28500000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.9 \cdot 10^{-103}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.9 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{-118}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -9 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-189}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -9e-87)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4.8e-189)
       t_0
       (if (<= B -4.3e-237)
         (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
         (if (<= B 9.6e-241)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (if (<= B 4.2e-101)
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
             (if (<= B 2.6e+36) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (B <= -9e-87) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4.8e-189) {
		tmp = t_0;
	} else if (B <= -4.3e-237) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 9.6e-241) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 4.2e-101) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.6e+36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (B <= -9e-87) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4.8e-189) {
		tmp = t_0;
	} else if (B <= -4.3e-237) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 9.6e-241) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 4.2e-101) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.6e+36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if B <= -9e-87:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4.8e-189:
		tmp = t_0
	elif B <= -4.3e-237:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 9.6e-241:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 4.2e-101:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.6e+36:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (B <= -9e-87)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4.8e-189)
		tmp = t_0;
	elseif (B <= -4.3e-237)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 9.6e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 4.2e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.6e+36)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (B <= -9e-87)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4.8e-189)
		tmp = t_0;
	elseif (B <= -4.3e-237)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 9.6e-241)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 4.2e-101)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.6e+36)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9e-87], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.8e-189], t$95$0, If[LessEqual[B, -4.3e-237], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.6e-241], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e-101], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e+36], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -8.99999999999999915e-87

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

   if -8.99999999999999915e-87 < B < -4.7999999999999997e-189 or 4.20000000000000031e-101 < B < 2.6000000000000001e36

   1. Initial program 38.8%

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

   3. Taylor expanded in C around inf 48.7%

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

   4. Taylor expanded in A around inf 48.7%

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

   if -4.7999999999999997e-189 < B < -4.29999999999999982e-237

   1. Initial program 73.6%

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

   3. Taylor expanded in C around -inf 72.3%

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

   if -4.29999999999999982e-237 < B < 9.6e-241

   1. Initial program 57.1%

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

   3. Taylor expanded in C around inf 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 49.1%

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

      2. distribute-rgt1-in 49.1%

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

      3. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 9.6e-241 < B < 4.20000000000000031e-101

   1. Initial program 63.4%

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

   3. Taylor expanded in A around inf 46.6%

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

   if 2.6000000000000001e36 < B

   1. Initial program 48.5%

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

   3. Taylor expanded in B around inf 69.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.1 \cdot 10^{-192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.15e-81)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -6.1e-192)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (if (<= B -2.25e-238)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (if (<= B 5.4e-241)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 8.8e-111)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (<= B 4.6e+69)
             (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-81) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6.1e-192) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -2.25e-238) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 5.4e-241) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 8.8e-111) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 4.6e+69) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-81) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6.1e-192) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -2.25e-238) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 5.4e-241) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 8.8e-111) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 4.6e+69) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.15e-81:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6.1e-192:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -2.25e-238:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 5.4e-241:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 8.8e-111:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 4.6e+69:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.15e-81)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6.1e-192)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -2.25e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 5.4e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 8.8e-111)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 4.6e+69)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.15e-81)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6.1e-192)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -2.25e-238)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 5.4e-241)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 8.8e-111)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 4.6e+69)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.15e-81], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.1e-192], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.25e-238], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.4e-241], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.8e-111], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e+69], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -1.14999999999999996e-81

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

   if -1.14999999999999996e-81 < B < -6.0999999999999999e-192

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

   4. Taylor expanded in A around inf 54.6%

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

   if -6.0999999999999999e-192 < B < -2.24999999999999998e-238

   1. Initial program 73.6%

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

   3. Taylor expanded in C around -inf 72.3%

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

   if -2.24999999999999998e-238 < B < 5.3999999999999998e-241

   1. Initial program 57.1%

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

   3. Taylor expanded in C around inf 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 49.1%

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

      2. distribute-rgt1-in 49.1%

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

      3. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 5.3999999999999998e-241 < B < 8.8e-111

   1. Initial program 64.3%

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

   3. Taylor expanded in A around inf 49.5%

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

   if 8.8e-111 < B < 4.60000000000000033e69

   1. Initial program 44.6%

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

   3. Taylor expanded in A around -inf 47.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 47.6%

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

   5. Simplified 47.6%

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

   if 4.60000000000000033e69 < B

   1. Initial program 44.5%

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

   3. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.1 \cdot 10^{-192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{+69}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-83)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -7.4e-189)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (if (<= B -9.8e-238)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (if (<= B 7.2e-242)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 8.5e-111)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (<= B 4.7e+69)
             (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-83) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.4e-189) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -9.8e-238) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 7.2e-242) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 8.5e-111) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 4.7e+69) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-83) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.4e-189) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -9.8e-238) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 7.2e-242) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 8.5e-111) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 4.7e+69) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.9e-83:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.4e-189:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -9.8e-238:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 7.2e-242:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 8.5e-111:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 4.7e+69:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.9e-83)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.4e-189)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -9.8e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 7.2e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 8.5e-111)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 4.7e+69)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.9e-83)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.4e-189)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -9.8e-238)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 7.2e-242)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 8.5e-111)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 4.7e+69)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e-83], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.4e-189], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.8e-238], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-242], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-111], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.7e+69], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -1.89999999999999988e-83

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

   if -1.89999999999999988e-83 < B < -7.40000000000000039e-189

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

   4. Taylor expanded in A around inf 54.6%

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

   if -7.40000000000000039e-189 < B < -9.7999999999999996e-238

   1. Initial program 73.6%

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

   3. Taylor expanded in C around -inf 72.3%

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

   if -9.7999999999999996e-238 < B < 7.20000000000000028e-242

   1. Initial program 57.1%

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

   3. Taylor expanded in C around inf 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 49.1%

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

      2. distribute-rgt1-in 49.1%

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

      3. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 7.20000000000000028e-242 < B < 8.5000000000000003e-111

   1. Initial program 64.3%

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

   3. Taylor expanded in A around inf 49.5%

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

   if 8.5000000000000003e-111 < B < 4.69999999999999996e69

   1. Initial program 44.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 44.6%

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

      2. associate-*l/ 44.6%

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

      3. *-un-lft-identity 44.6%

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

      4. unpow2 44.6%

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

      5. unpow2 44.6%

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

      6. hypot-define 56.5%

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

   4. Applied egg-rr 56.5%

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

   5. Taylor expanded in A around -inf 47.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 47.5%

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

      2. associate-/l* 47.6%

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

   7. Applied egg-rr 47.6%

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

   if 4.69999999999999996e69 < B

   1. Initial program 44.5%

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

   3. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{+69}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.54 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq -7.1 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.2e-80)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.54e-189)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (<= B -7.1e-239)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (if (<= B 2.25e-241)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 1.3e-110)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (<= B 4.6e+69)
             (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-80) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.54e-189) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= -7.1e-239) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 2.25e-241) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.3e-110) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 4.6e+69) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-80) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.54e-189) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= -7.1e-239) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 2.25e-241) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.3e-110) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 4.6e+69) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.2e-80:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.54e-189:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= -7.1e-239:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 2.25e-241:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.3e-110:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 4.6e+69:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.2e-80)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.54e-189)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= -7.1e-239)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 2.25e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.3e-110)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 4.6e+69)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.2e-80)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.54e-189)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= -7.1e-239)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 2.25e-241)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.3e-110)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 4.6e+69)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.2e-80], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.54e-189], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.1e-239], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.25e-241], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-110], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e+69], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -1.2e-80

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

   if -1.2e-80 < B < -1.54000000000000005e-189

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

   4. Taylor expanded in A around inf 54.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. *-commutative 54.6%

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

      2. associate-*l/ 54.5%

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

      3. +-rgt-identity 54.5%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C} + 0\right)} \cdot 180}{\pi} \]

      4. fma-define 54.5%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)} \cdot 180}{\pi} \]

      5. mul0-lft 43.3%

         \[\leadsto \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \color{blue}{0 \cdot \frac{A}{B}}\right)\right) \cdot 180}{\pi} \]

      6. associate-/l* 43.4%

         \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0 \cdot \frac{A}{B}\right)\right) \cdot \frac{180}{\pi}} \]

   6. Simplified 54.7%

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

   if -1.54000000000000005e-189 < B < -7.0999999999999997e-239

   1. Initial program 73.6%

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

   3. Taylor expanded in C around -inf 72.3%

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

   if -7.0999999999999997e-239 < B < 2.2499999999999999e-241

   1. Initial program 57.1%

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

   3. Taylor expanded in C around inf 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 49.1%

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

      2. distribute-rgt1-in 49.1%

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

      3. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 49.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 49.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 2.2499999999999999e-241 < B < 1.29999999999999995e-110

   1. Initial program 64.3%

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

   3. Taylor expanded in A around inf 49.5%

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

   if 1.29999999999999995e-110 < B < 4.60000000000000033e69

   1. Initial program 44.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 44.6%

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

      2. associate-*l/ 44.6%

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

      3. *-un-lft-identity 44.6%

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

      4. unpow2 44.6%

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

      5. unpow2 44.6%

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

      6. hypot-define 56.5%

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

   4. Applied egg-rr 56.5%

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

   5. Taylor expanded in A around -inf 47.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 47.5%

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

      2. associate-/l* 47.6%

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

   7. Applied egg-rr 47.6%

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

   if 4.60000000000000033e69 < B

   1. Initial program 44.5%

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

   3. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.54 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq -7.1 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.95 \cdot 10^{+123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.5 \cdot 10^{+83}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq -1.1 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -1.18 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)))
   (if (<= C -1.95e+123)
     (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
     (if (<= C -6.5e+83)
       (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
       (if (<= C -1.1e+22)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C -1.18e-54)
           t_0
           (if (<= C -1.05e-142)
             (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
             (if (<= C 1.9e+16)
               t_0
               (/ (atan (/ (* B -0.5) C)) (* PI 0.005555555555555556))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	double tmp;
	if (C <= -1.95e+123) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (C <= -6.5e+83) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (C <= -1.1e+22) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= -1.18e-54) {
		tmp = t_0;
	} else if (C <= -1.05e-142) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 1.9e+16) {
		tmp = t_0;
	} else {
		tmp = atan(((B * -0.5) / C)) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	double tmp;
	if (C <= -1.95e+123) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (C <= -6.5e+83) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (C <= -1.1e+22) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= -1.18e-54) {
		tmp = t_0;
	} else if (C <= -1.05e-142) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 1.9e+16) {
		tmp = t_0;
	} else {
		tmp = Math.atan(((B * -0.5) / C)) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	tmp = 0
	if C <= -1.95e+123:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif C <= -6.5e+83:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif C <= -1.1e+22:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= -1.18e-54:
		tmp = t_0
	elif C <= -1.05e-142:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 1.9e+16:
		tmp = t_0
	else:
		tmp = math.atan(((B * -0.5) / C)) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi)
	tmp = 0.0
	if (C <= -1.95e+123)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (C <= -6.5e+83)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (C <= -1.1e+22)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= -1.18e-54)
		tmp = t_0;
	elseif (C <= -1.05e-142)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 1.9e+16)
		tmp = t_0;
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / C)) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((1.0 - (A / B)))) / pi;
	tmp = 0.0;
	if (C <= -1.95e+123)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (C <= -6.5e+83)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (C <= -1.1e+22)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= -1.18e-54)
		tmp = t_0;
	elseif (C <= -1.05e-142)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 1.9e+16)
		tmp = t_0;
	else
		tmp = atan(((B * -0.5) / C)) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -1.95e+123], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -6.5e+83], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.1e+22], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.18e-54], t$95$0, If[LessEqual[C, -1.05e-142], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.9e+16], t$95$0, N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if C < -1.94999999999999996e123

   1. Initial program 81.6%

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

   3. Taylor expanded in C around -inf 77.9%

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

   if -1.94999999999999996e123 < C < -6.5000000000000003e83

   1. Initial program 31.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 31.8%

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

      2. associate-*l/ 31.8%

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

      3. *-un-lft-identity 31.8%

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

      4. unpow2 31.8%

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

      5. unpow2 31.8%

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

      6. hypot-define 64.3%

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

   4. Applied egg-rr 64.3%

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

   5. Taylor expanded in A around -inf 67.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 67.4%

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

      2. associate-/l* 67.4%

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

   7. Applied egg-rr 67.4%

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

   if -6.5000000000000003e83 < C < -1.1e22

   1. Initial program 74.1%

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

   3. Taylor expanded in B around inf 55.3%

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

   if -1.1e22 < C < -1.17999999999999996e-54 or -1.05e-142 < C < 1.9e16

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 59.6%

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

      2. associate-*l/ 59.6%

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

      3. *-un-lft-identity 59.6%

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

      4. unpow2 59.6%

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

      5. unpow2 59.6%

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

      6. hypot-define 84.3%

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in C around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac2 58.1%

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

      3. unpow2 58.1%

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

      4. unpow2 58.1%

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

      5. hypot-define 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in B around -inf 57.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. neg-mul-1 57.5%

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

      2. unsub-neg 57.5%

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

   10. Simplified 57.5%

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

   if -1.17999999999999996e-54 < C < -1.05e-142

   1. Initial program 56.6%

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

   3. Taylor expanded in A around -inf 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 53.9%

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

   5. Simplified 53.9%

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

   if 1.9e16 < C

   1. Initial program 19.8%

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

   3. Taylor expanded in C around inf 68.1%

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

   4. Taylor expanded in A around inf 68.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

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

      2. associate-*l/ 68.2%

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

      3. +-rgt-identity 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C} + 0\right)} \cdot 180}{\pi} \]

      4. fma-define 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)} \cdot 180}{\pi} \]

      5. mul0-lft 65.0%

         \[\leadsto \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \color{blue}{0 \cdot \frac{A}{B}}\right)\right) \cdot 180}{\pi} \]

      6. associate-/l* 65.0%

         \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0 \cdot \frac{A}{B}\right)\right) \cdot \frac{180}{\pi}} \]

   6. Simplified 68.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
   7. Step-by-step derivation

      1. clear-num 68.1%

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

      2. un-div-inv 68.1%

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

      3. associate-*r/ 68.2%

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

      4. div-inv 68.2%

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

      5. metadata-eval 68.2%

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

   8. Applied egg-rr 68.2%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.95 \cdot 10^{+123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.5 \cdot 10^{+83}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq -1.1 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -1.18 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;C \leq -6500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq -1.6 \cdot 10^{-78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1.4 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI))
        (t_1 (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)))
   (if (<= C -6500000000.0)
     t_1
     (if (<= C -1.6e-78)
       t_0
       (if (<= C -1.4e-103)
         t_1
         (if (<= C -1.9e-139)
           (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
           (if (<= C 1.85e+17)
             t_0
             (/ (atan (/ (* B -0.5) C)) (* PI 0.005555555555555556)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	double t_1 = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	double tmp;
	if (C <= -6500000000.0) {
		tmp = t_1;
	} else if (C <= -1.6e-78) {
		tmp = t_0;
	} else if (C <= -1.4e-103) {
		tmp = t_1;
	} else if (C <= -1.9e-139) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 1.85e+17) {
		tmp = t_0;
	} else {
		tmp = atan(((B * -0.5) / C)) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	double t_1 = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	double tmp;
	if (C <= -6500000000.0) {
		tmp = t_1;
	} else if (C <= -1.6e-78) {
		tmp = t_0;
	} else if (C <= -1.4e-103) {
		tmp = t_1;
	} else if (C <= -1.9e-139) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 1.85e+17) {
		tmp = t_0;
	} else {
		tmp = Math.atan(((B * -0.5) / C)) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	t_1 = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	tmp = 0
	if C <= -6500000000.0:
		tmp = t_1
	elif C <= -1.6e-78:
		tmp = t_0
	elif C <= -1.4e-103:
		tmp = t_1
	elif C <= -1.9e-139:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 1.85e+17:
		tmp = t_0
	else:
		tmp = math.atan(((B * -0.5) / C)) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi)
	t_1 = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi)
	tmp = 0.0
	if (C <= -6500000000.0)
		tmp = t_1;
	elseif (C <= -1.6e-78)
		tmp = t_0;
	elseif (C <= -1.4e-103)
		tmp = t_1;
	elseif (C <= -1.9e-139)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 1.85e+17)
		tmp = t_0;
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / C)) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((1.0 - (A / B)))) / pi;
	t_1 = (180.0 * atan(((C / B) + -1.0))) / pi;
	tmp = 0.0;
	if (C <= -6500000000.0)
		tmp = t_1;
	elseif (C <= -1.6e-78)
		tmp = t_0;
	elseif (C <= -1.4e-103)
		tmp = t_1;
	elseif (C <= -1.9e-139)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 1.85e+17)
		tmp = t_0;
	else
		tmp = atan(((B * -0.5) / C)) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -6500000000.0], t$95$1, If[LessEqual[C, -1.6e-78], t$95$0, If[LessEqual[C, -1.4e-103], t$95$1, If[LessEqual[C, -1.9e-139], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e+17], t$95$0, N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -6.5e9 or -1.6e-78 < C < -1.40000000000000011e-103

   1. Initial program 73.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 73.0%

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

      2. associate-*l/ 73.0%

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

      3. *-un-lft-identity 73.0%

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

      4. unpow2 73.0%

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

      5. unpow2 73.0%

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

      6. hypot-define 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in B around inf 77.4%

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

      1. +-commutative 77.4%

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

      2. associate--r+ 77.4%

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

      3. div-sub 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in C around inf 77.8%

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

   if -6.5e9 < C < -1.6e-78 or -1.90000000000000004e-139 < C < 1.85e17

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 59.6%

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

      2. associate-*l/ 59.6%

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

      3. *-un-lft-identity 59.6%

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

      4. unpow2 59.6%

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

      5. unpow2 59.6%

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

      6. hypot-define 84.6%

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

   4. Applied egg-rr 84.6%

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

   5. Taylor expanded in C around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-neg-frac2 57.3%

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

      3. unpow2 57.3%

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

      4. unpow2 57.3%

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

      5. hypot-define 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in B around -inf 57.6%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. neg-mul-1 57.6%

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

      2. unsub-neg 57.6%

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

   10. Simplified 57.6%

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

   if -1.40000000000000011e-103 < C < -1.90000000000000004e-139

   1. Initial program 53.0%

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

   3. Taylor expanded in A around -inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 63.3%

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

   5. Simplified 63.3%

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

   if 1.85e17 < C

   1. Initial program 19.8%

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

   3. Taylor expanded in C around inf 68.1%

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

   4. Taylor expanded in A around inf 68.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. *-commutative 68.1%

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

      2. associate-*l/ 68.2%

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

      3. +-rgt-identity 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C} + 0\right)} \cdot 180}{\pi} \]

      4. fma-define 68.2%

         \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)} \cdot 180}{\pi} \]

      5. mul0-lft 65.0%

         \[\leadsto \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \color{blue}{0 \cdot \frac{A}{B}}\right)\right) \cdot 180}{\pi} \]

      6. associate-/l* 65.0%

         \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0 \cdot \frac{A}{B}\right)\right) \cdot \frac{180}{\pi}} \]

   6. Simplified 68.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
   7. Step-by-step derivation

      1. clear-num 68.1%

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

      2. un-div-inv 68.1%

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

      3. associate-*r/ 68.2%

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

      4. div-inv 68.2%

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

      5. metadata-eval 68.2%

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

   8. Applied egg-rr 68.2%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -6500000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.85 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-49}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{+27}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.85e-277)
     (/ (* 180.0 (atan (+ 1.0 t_0))) PI)
     (if (<= B 8e-244)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.35e-49)
         (/ (* 180.0 (atan (+ t_0 -1.0))) PI)
         (if (<= B 3.6e+27)
           (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
           (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.85e-277) {
		tmp = (180.0 * atan((1.0 + t_0))) / ((double) M_PI);
	} else if (B <= 8e-244) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.35e-49) {
		tmp = (180.0 * atan((t_0 + -1.0))) / ((double) M_PI);
	} else if (B <= 3.6e+27) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.85e-277) {
		tmp = (180.0 * Math.atan((1.0 + t_0))) / Math.PI;
	} else if (B <= 8e-244) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.35e-49) {
		tmp = (180.0 * Math.atan((t_0 + -1.0))) / Math.PI;
	} else if (B <= 3.6e+27) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.85e-277:
		tmp = (180.0 * math.atan((1.0 + t_0))) / math.pi
	elif B <= 8e-244:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.35e-49:
		tmp = (180.0 * math.atan((t_0 + -1.0))) / math.pi
	elif B <= 3.6e+27:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.85e-277)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + t_0))) / pi);
	elseif (B <= 8e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.35e-49)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + -1.0))) / pi);
	elseif (B <= 3.6e+27)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.85e-277)
		tmp = (180.0 * atan((1.0 + t_0))) / pi;
	elseif (B <= 8e-244)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.35e-49)
		tmp = (180.0 * atan((t_0 + -1.0))) / pi;
	elseif (B <= 3.6e+27)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.85e-277], N[(N[(180.0 * N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8e-244], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-49], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.6e+27], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.84999999999999992e-277

   1. Initial program 54.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.8%

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

      3. *-un-lft-identity 54.8%

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

      4. unpow2 54.8%

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

      5. unpow2 54.8%

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

      6. hypot-define 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in B around -inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -1.84999999999999992e-277 < B < 7.9999999999999994e-244

   1. Initial program 61.7%

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

   3. Taylor expanded in C around inf 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.3%

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

      2. distribute-rgt1-in 68.3%

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

      3. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 7.9999999999999994e-244 < B < 1.35e-49

   1. Initial program 59.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 59.9%

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

      2. associate-*l/ 59.9%

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

      3. *-un-lft-identity 59.9%

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

      4. unpow2 59.9%

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

      5. unpow2 59.9%

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

      6. hypot-define 78.9%

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

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in B around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. associate--r+ 56.7%

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

      3. div-sub 59.5%

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

   7. Simplified 59.5%

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

   if 1.35e-49 < B < 3.59999999999999983e27

   1. Initial program 26.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 26.3%

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

      2. associate-*l/ 26.3%

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

      3. *-un-lft-identity 26.3%

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

      4. unpow2 26.3%

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

      5. unpow2 26.3%

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

      6. hypot-define 38.6%

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

   4. Applied egg-rr 38.6%

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

   5. Taylor expanded in A around -inf 54.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 54.5%

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

      2. associate-/l* 54.6%

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

   7. Applied egg-rr 54.6%

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

   if 3.59999999999999983e27 < B

   1. Initial program 49.4%

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

   3. Taylor expanded in B around inf 85.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.85 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-49}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{+27}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.62 \cdot 10^{-49} \lor \neg \left(B \leq 3.6 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -8.5e-277)
     (/ (* 180.0 (atan (+ 1.0 t_0))) PI)
     (if (<= B 8.5e-244)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (or (<= B 1.62e-49) (not (<= B 3.6e+27)))
         (/ (* 180.0 (atan (+ t_0 -1.0))) PI)
         (* (atan (* 0.5 (/ B A))) (/ 180.0 PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -8.5e-277) {
		tmp = (180.0 * atan((1.0 + t_0))) / ((double) M_PI);
	} else if (B <= 8.5e-244) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if ((B <= 1.62e-49) || !(B <= 3.6e+27)) {
		tmp = (180.0 * atan((t_0 + -1.0))) / ((double) M_PI);
	} else {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -8.5e-277) {
		tmp = (180.0 * Math.atan((1.0 + t_0))) / Math.PI;
	} else if (B <= 8.5e-244) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if ((B <= 1.62e-49) || !(B <= 3.6e+27)) {
		tmp = (180.0 * Math.atan((t_0 + -1.0))) / Math.PI;
	} else {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -8.5e-277:
		tmp = (180.0 * math.atan((1.0 + t_0))) / math.pi
	elif B <= 8.5e-244:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif (B <= 1.62e-49) or not (B <= 3.6e+27):
		tmp = (180.0 * math.atan((t_0 + -1.0))) / math.pi
	else:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -8.5e-277)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + t_0))) / pi);
	elseif (B <= 8.5e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif ((B <= 1.62e-49) || !(B <= 3.6e+27))
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + -1.0))) / pi);
	else
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -8.5e-277)
		tmp = (180.0 * atan((1.0 + t_0))) / pi;
	elseif (B <= 8.5e-244)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif ((B <= 1.62e-49) || ~((B <= 3.6e+27)))
		tmp = (180.0 * atan((t_0 + -1.0))) / pi;
	else
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -8.5e-277], N[(N[(180.0 * N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.5e-244], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.62e-49], N[Not[LessEqual[B, 3.6e+27]], $MachinePrecision]], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.4999999999999998e-277

   1. Initial program 54.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.8%

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

      3. *-un-lft-identity 54.8%

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

      4. unpow2 54.8%

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

      5. unpow2 54.8%

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

      6. hypot-define 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in B around -inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -8.4999999999999998e-277 < B < 8.4999999999999999e-244

   1. Initial program 61.7%

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

   3. Taylor expanded in C around inf 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.3%

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

      2. distribute-rgt1-in 68.3%

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

      3. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 8.4999999999999999e-244 < B < 1.62e-49 or 3.59999999999999983e27 < B

   1. Initial program 53.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 53.3%

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

      2. associate-*l/ 53.3%

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

      3. *-un-lft-identity 53.3%

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

      4. unpow2 53.3%

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

      5. unpow2 53.3%

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

      6. hypot-define 83.4%

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

   4. Applied egg-rr 83.4%

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

   5. Taylor expanded in B around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. associate--r+ 74.6%

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

      3. div-sub 75.6%

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

   7. Simplified 75.6%

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

   if 1.62e-49 < B < 3.59999999999999983e27

   1. Initial program 26.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 26.3%

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

      2. associate-*l/ 26.3%

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

      3. *-un-lft-identity 26.3%

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

      4. unpow2 26.3%

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

      5. unpow2 26.3%

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

      6. hypot-define 38.6%

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

   4. Applied egg-rr 38.6%

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

   5. Taylor expanded in A around -inf 54.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 54.5%

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

      2. associate-/l* 54.6%

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

   7. Applied egg-rr 54.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.62 \cdot 10^{-49} \lor \neg \left(B \leq 3.6 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.45 \cdot 10^{-99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -2.6e-84)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 6e-242)
       t_0
       (if (<= B 3.45e-99)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= B 3.4e+36) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (B <= -2.6e-84) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6e-242) {
		tmp = t_0;
	} else if (B <= 3.45e-99) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 3.4e+36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (B <= -2.6e-84) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6e-242) {
		tmp = t_0;
	} else if (B <= 3.45e-99) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 3.4e+36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if B <= -2.6e-84:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6e-242:
		tmp = t_0
	elif B <= 3.45e-99:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 3.4e+36:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (B <= -2.6e-84)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6e-242)
		tmp = t_0;
	elseif (B <= 3.45e-99)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 3.4e+36)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (B <= -2.6e-84)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6e-242)
		tmp = t_0;
	elseif (B <= 3.45e-99)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 3.4e+36)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.6e-84], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6e-242], t$95$0, If[LessEqual[B, 3.45e-99], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.4e+36], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.6e-84

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

   if -2.6e-84 < B < 6e-242 or 3.4500000000000002e-99 < B < 3.3999999999999998e36

   1. Initial program 47.9%

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

   3. Taylor expanded in C around inf 44.0%

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

   4. Taylor expanded in A around inf 44.0%

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

   if 6e-242 < B < 3.4500000000000002e-99

   1. Initial program 63.4%

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

   3. Taylor expanded in A around inf 46.6%

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

   if 3.3999999999999998e36 < B

   1. Initial program 48.5%

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

   3. Taylor expanded in B around inf 69.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.45 \cdot 10^{-99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -7.2 \cdot 10^{-277}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -7.2e-277)
     t_0
     (if (<= B 4.6e-241)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.4e-105)
         t_0
         (if (<= B 2.1e+30)
           (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
           (/ (* -180.0 (atan (+ 1.0 (/ A B)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -7.2e-277) {
		tmp = t_0;
	} else if (B <= 4.6e-241) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.4e-105) {
		tmp = t_0;
	} else if (B <= 2.1e+30) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan((1.0 + (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -7.2e-277) {
		tmp = t_0;
	} else if (B <= 4.6e-241) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.4e-105) {
		tmp = t_0;
	} else if (B <= 2.1e+30) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan((1.0 + (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -7.2e-277:
		tmp = t_0
	elif B <= 4.6e-241:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.4e-105:
		tmp = t_0
	elif B <= 2.1e+30:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = (-180.0 * math.atan((1.0 + (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -7.2e-277)
		tmp = t_0;
	elseif (B <= 4.6e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.4e-105)
		tmp = t_0;
	elseif (B <= 2.1e+30)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(1.0 + Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -7.2e-277)
		tmp = t_0;
	elseif (B <= 4.6e-241)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.4e-105)
		tmp = t_0;
	elseif (B <= 2.1e+30)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = (-180.0 * atan((1.0 + (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7.2e-277], t$95$0, If[LessEqual[B, 4.6e-241], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-105], t$95$0, If[LessEqual[B, 2.1e+30], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.19999999999999968e-277 or 4.5999999999999999e-241 < B < 1.4e-105

   1. Initial program 56.5%

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

   3. Taylor expanded in B around -inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. div-sub 68.9%

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

   5. Simplified 68.9%

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

   if -7.19999999999999968e-277 < B < 4.5999999999999999e-241

   1. Initial program 61.7%

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

   3. Taylor expanded in C around inf 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.3%

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

      2. distribute-rgt1-in 68.3%

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

      3. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 1.4e-105 < B < 2.1e30

   1. Initial program 33.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 33.3%

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

      2. associate-*l/ 33.3%

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

      3. *-un-lft-identity 33.3%

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

      4. unpow2 33.3%

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

      5. unpow2 33.3%

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

      6. hypot-define 48.5%

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

   4. Applied egg-rr 48.5%

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

   5. Taylor expanded in A around -inf 47.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-/l* 47.9%

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

   7. Applied egg-rr 47.9%

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

   if 2.1e30 < B

   1. Initial program 49.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 49.4%

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

      2. associate-*l/ 49.4%

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

      3. *-un-lft-identity 49.4%

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

      4. unpow2 49.4%

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

      5. unpow2 49.4%

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

      6. hypot-define 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in C around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. distribute-neg-frac2 42.5%

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

      3. unpow2 42.5%

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

      4. unpow2 42.5%

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

      5. hypot-define 77.9%

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

   7. Simplified 77.9%

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

      1. distribute-frac-neg2 77.9%

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

      2. atan-neg 77.9%

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

      3. add-sqr-sqrt 77.6%

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

      4. sqrt-unprod 28.6%

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

      5. sqr-neg 28.6%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 1.8%

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

      8. distribute-rgt-neg-in 1.8%

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

      9. neg-sub0 1.8%

         \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}}{\pi} \]

      10. add-sqr-sqrt 0.0%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{-B} \cdot \sqrt{-B}}}\right)}{\pi} \]

      11. sqrt-unprod 28.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{\left(-B\right) \cdot \left(-B\right)}}}\right)}{\pi} \]

      12. sqr-neg 28.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\sqrt{\color{blue}{B \cdot B}}}\right)}{\pi} \]

      13. sqrt-unprod 77.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}\right)}{\pi} \]

      14. add-sqr-sqrt 77.9%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{B}}\right)}{\pi} \]

   9. Applied egg-rr 77.9%

      \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. neg-sub0 77.9%

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

       2. *-commutative 77.9%

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

       3. distribute-rgt-neg-in 77.9%

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

       4. *-lft-identity 77.9%

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

       5. *-lft-identity 77.9%

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

       6. hypot-undefine 42.5%

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

       7. unpow2 42.5%

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

       8. unpow2 42.5%

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

       9. +-commutative 42.5%

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

       10. unpow2 42.5%

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

       11. unpow2 42.5%

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

       12. hypot-define 77.9%

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

       13. metadata-eval 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in A around 0 77.2%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(1 + \frac{A}{B}\right)} \cdot -180}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-277}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (+ 1.0 (/ (- C A) B)))))
   (if (<= B -1.9e-275)
     (/ (* 180.0 t_0) PI)
     (if (<= B 1.4e-242)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.45e-105)
         (* 180.0 (/ t_0 PI))
         (if (<= B 1.4e+33)
           (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
           (/ (* -180.0 (atan (+ 1.0 (/ A B)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((1.0 + ((C - A) / B)));
	double tmp;
	if (B <= -1.9e-275) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else if (B <= 1.4e-242) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.45e-105) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (B <= 1.4e+33) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan((1.0 + (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((1.0 + ((C - A) / B)));
	double tmp;
	if (B <= -1.9e-275) {
		tmp = (180.0 * t_0) / Math.PI;
	} else if (B <= 1.4e-242) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.45e-105) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (B <= 1.4e+33) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan((1.0 + (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((1.0 + ((C - A) / B)))
	tmp = 0
	if B <= -1.9e-275:
		tmp = (180.0 * t_0) / math.pi
	elif B <= 1.4e-242:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.45e-105:
		tmp = 180.0 * (t_0 / math.pi)
	elif B <= 1.4e+33:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	else:
		tmp = (-180.0 * math.atan((1.0 + (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(1.0 + Float64(Float64(C - A) / B)))
	tmp = 0.0
	if (B <= -1.9e-275)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	elseif (B <= 1.4e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.45e-105)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (B <= 1.4e+33)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(1.0 + Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((1.0 + ((C - A) / B)));
	tmp = 0.0;
	if (B <= -1.9e-275)
		tmp = (180.0 * t_0) / pi;
	elseif (B <= 1.4e-242)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.45e-105)
		tmp = 180.0 * (t_0 / pi);
	elseif (B <= 1.4e+33)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = (-180.0 * atan((1.0 + (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[B, -1.9e-275], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.4e-242], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-105], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e+33], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.89999999999999986e-275

   1. Initial program 54.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.8%

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

      3. *-un-lft-identity 54.8%

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

      4. unpow2 54.8%

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

      5. unpow2 54.8%

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

      6. hypot-define 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in B around -inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -1.89999999999999986e-275 < B < 1.39999999999999992e-242

   1. Initial program 61.7%

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

   3. Taylor expanded in C around inf 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.3%

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

      2. distribute-rgt1-in 68.3%

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

      3. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 1.39999999999999992e-242 < B < 1.45000000000000002e-105

   1. Initial program 64.3%

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

   3. Taylor expanded in B around -inf 56.7%

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

      1. associate--l+ 56.7%

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

      2. div-sub 60.4%

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

   5. Simplified 60.4%

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

   if 1.45000000000000002e-105 < B < 1.4e33

   1. Initial program 33.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 33.3%

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

      2. associate-*l/ 33.3%

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

      3. *-un-lft-identity 33.3%

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

      4. unpow2 33.3%

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

      5. unpow2 33.3%

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

      6. hypot-define 48.5%

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

   4. Applied egg-rr 48.5%

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

   5. Taylor expanded in A around -inf 47.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-/l* 47.9%

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

   7. Applied egg-rr 47.9%

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

   if 1.4e33 < B

   1. Initial program 49.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 49.4%

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

      2. associate-*l/ 49.4%

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

      3. *-un-lft-identity 49.4%

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

      4. unpow2 49.4%

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

      5. unpow2 49.4%

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

      6. hypot-define 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in C around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. distribute-neg-frac2 42.5%

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

      3. unpow2 42.5%

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

      4. unpow2 42.5%

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

      5. hypot-define 77.9%

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

   7. Simplified 77.9%

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

      1. distribute-frac-neg2 77.9%

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

      2. atan-neg 77.9%

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

      3. add-sqr-sqrt 77.6%

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

      4. sqrt-unprod 28.6%

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

      5. sqr-neg 28.6%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 1.8%

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

      8. distribute-rgt-neg-in 1.8%

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

      9. neg-sub0 1.8%

         \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}}{\pi} \]

      10. add-sqr-sqrt 0.0%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{-B} \cdot \sqrt{-B}}}\right)}{\pi} \]

      11. sqrt-unprod 28.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{\left(-B\right) \cdot \left(-B\right)}}}\right)}{\pi} \]

      12. sqr-neg 28.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\sqrt{\color{blue}{B \cdot B}}}\right)}{\pi} \]

      13. sqrt-unprod 77.6%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{\sqrt{B} \cdot \sqrt{B}}}\right)}{\pi} \]

      14. add-sqr-sqrt 77.9%

          \[\leadsto \frac{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{\color{blue}{B}}\right)}{\pi} \]

   9. Applied egg-rr 77.9%

      \[\leadsto \frac{\color{blue}{0 - 180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. neg-sub0 77.9%

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

       2. *-commutative 77.9%

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

       3. distribute-rgt-neg-in 77.9%

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

       4. *-lft-identity 77.9%

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

       5. *-lft-identity 77.9%

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

       6. hypot-undefine 42.5%

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

       7. unpow2 42.5%

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

       8. unpow2 42.5%

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

       9. +-commutative 42.5%

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

       10. unpow2 42.5%

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

       11. unpow2 42.5%

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

       12. hypot-define 77.9%

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

       13. metadata-eval 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in A around 0 77.2%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(1 + \frac{A}{B}\right)} \cdot -180}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.8e-95)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7e-240)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 3.6e+36)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.8e-95) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7e-240) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.6e+36) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.8e-95) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7e-240) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.6e+36) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.8e-95:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7e-240:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.6e+36:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.8e-95)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7e-240)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.6e+36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.8e-95)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7e-240)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.6e+36)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.8e-95], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-240], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e+36], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.8e-95

   1. Initial program 56.0%

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

   3. Taylor expanded in B around -inf 58.4%

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

   if -4.8e-95 < B < 7.00000000000000032e-240

   1. Initial program 54.6%

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

   3. Taylor expanded in C around inf 41.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 41.4%

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

      2. distribute-rgt1-in 41.4%

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

      3. metadata-eval 41.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 41.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 41.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 41.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 7.00000000000000032e-240 < B < 3.5999999999999997e36

   1. Initial program 50.1%

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

   3. Taylor expanded in A around inf 33.7%

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

   if 3.5999999999999997e36 < B

   1. Initial program 48.5%

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

   3. Taylor expanded in B around inf 69.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.1e-94)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.5e-29)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e-94) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.5e-29) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e-94) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.5e-29) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.1e-94:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.5e-29:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.1e-94)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.5e-29)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.1e-94)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.5e-29)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.1e-94], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-29], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.10000000000000001e-94

   1. Initial program 56.0%

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

   3. Taylor expanded in B around -inf 58.4%

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

   if -4.10000000000000001e-94 < B < 4.4999999999999998e-29

   1. Initial program 53.3%

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

   3. Taylor expanded in C around inf 32.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 32.7%

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

      2. distribute-rgt1-in 32.7%

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

      3. metadata-eval 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 32.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 4.4999999999999998e-29 < B

   1. Initial program 47.6%

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

   3. Taylor expanded in B around inf 60.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 54.3%

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

   3. Taylor expanded in B around -inf 44.7%

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

   if -4.999999999999985e-310 < B

   1. Initial program 51.1%

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

   3. Taylor expanded in B around inf 40.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.5% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.8%

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

3. Taylor expanded in B around inf 20.3%

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

4. Final simplification 20.3%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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)))