ABCF->ab-angle angle

Percentage Accurate: 53.9% → 81.4%

Time: 29.1s

Alternatives: 24

Speedup: 3.4×

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: 53.9% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.45e+190)
   (* (atan (/ (* B 0.5) 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 <= -1.45e+190) {
		tmp = atan(((B * 0.5) / 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 <= -1.45e+190) {
		tmp = Math.atan(((B * 0.5) / 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 <= -1.45e+190:
		tmp = math.atan(((B * 0.5) / 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 <= -1.45e+190)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / 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 <= -1.45e+190)
		tmp = atan(((B * 0.5) / 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, -1.45e+190], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $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 < -1.44999999999999995e190

   1. Initial program 5.6%

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

   3. Taylor expanded in A around -inf 91.5%

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

      1. associate-*r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in B around 0 91.5%

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

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-/l* 91.7%

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

      4. associate-*r/ 91.7%

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

      5. *-commutative 91.7%

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

   8. Simplified 91.7%

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

   if -1.44999999999999995e190 < A

   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. Step-by-step derivation

      1. associate-*r/ 56.5%

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

      2. associate-*l/ 56.5%

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

      3. *-un-lft-identity 56.5%

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

      4. unpow2 56.5%

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

      5. unpow2 56.5%

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

      6. hypot-define 80.5%

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

   4. Applied egg-rr 80.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.4e-147)
   (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
   (if (<= C 2.8e+58)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-147) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else if (C <= 2.8e+58) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-147) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else if (C <= 2.8e+58) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.4e-147:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	elif C <= 2.8e+58:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.4e-147)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	elseif (C <= 2.8e+58)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.4e-147)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	elseif (C <= 2.8e+58)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.4e-147], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.8e+58], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.4e-147

   1. Initial program 67.4%

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

   3. Taylor expanded in B around 0 67.4%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in A around 0 67.4%

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

      1. unpow2 67.4%

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

      2. unpow2 67.4%

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

      3. hypot-define 86.2%

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

   8. Simplified 86.2%

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

   if -1.4e-147 < C < 2.7999999999999998e58

   1. Initial program 51.3%

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

   3. Taylor expanded in C around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. distribute-neg-frac2 50.3%

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

      3. +-commutative 50.3%

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

      4. unpow2 50.3%

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

      5. unpow2 50.3%

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

      6. hypot-define 74.9%

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

   5. Simplified 74.9%

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

   if 2.7999999999999998e58 < C

   1. Initial program 16.9%

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

      1. associate-*r/ 16.9%

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

      2. associate-*l/ 16.9%

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

      3. *-un-lft-identity 16.9%

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

      4. unpow2 16.9%

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

      5. unpow2 16.9%

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

      6. hypot-define 51.2%

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

   4. Applied egg-rr 51.2%

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

   5. Taylor expanded in C around inf 76.9%

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

   6. Taylor expanded in A around inf 76.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5e-147)
   (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
   (if (<= C 3.7e+59)
     (* (/ 180.0 PI) (atan (/ (- (- A) (hypot A B)) B)))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-147) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else if (C <= 3.7e+59) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-A - hypot(A, B)) / B));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-147) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else if (C <= 3.7e+59) {
		tmp = (180.0 / Math.PI) * Math.atan(((-A - Math.hypot(A, B)) / B));
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5e-147:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	elif C <= 3.7e+59:
		tmp = (180.0 / math.pi) * math.atan(((-A - math.hypot(A, B)) / B))
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5e-147)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	elseif (C <= 3.7e+59)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5e-147)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	elseif (C <= 3.7e+59)
		tmp = (180.0 / pi) * atan(((-A - hypot(A, B)) / B));
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5e-147], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.7e+59], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -5.00000000000000013e-147

   1. Initial program 67.4%

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

   3. Taylor expanded in B around 0 67.4%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in A around 0 67.4%

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

      1. unpow2 67.4%

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

      2. unpow2 67.4%

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

      3. hypot-define 86.2%

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

   8. Simplified 86.2%

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

   if -5.00000000000000013e-147 < C < 3.69999999999999997e59

   1. Initial program 51.3%

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

   3. Taylor expanded in B around 0 49.6%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in C around 0 50.3%

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

      1. distribute-lft-in 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. mul-1-neg 50.3%

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

      5. unpow2 50.3%

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

      6. unpow2 50.3%

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

      7. hypot-define 74.9%

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

   8. Simplified 74.9%

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

   if 3.69999999999999997e59 < C

   1. Initial program 16.9%

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

      1. associate-*r/ 16.9%

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

      2. associate-*l/ 16.9%

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

      3. *-un-lft-identity 16.9%

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

      4. unpow2 16.9%

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

      5. unpow2 16.9%

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

      6. hypot-define 51.2%

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

   4. Applied egg-rr 51.2%

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

   5. Taylor expanded in C around inf 76.9%

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

   6. Taylor expanded in A around inf 76.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - \frac{\mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{+55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.9e-147)
   (/ (* 180.0 (atan (- (/ C B) (/ (hypot B C) B)))) PI)
   (if (<= C 1e+55)
     (* (/ 180.0 PI) (atan (/ (- (- A) (hypot A B)) B)))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.9e-147) {
		tmp = (180.0 * atan(((C / B) - (hypot(B, C) / B)))) / ((double) M_PI);
	} else if (C <= 1e+55) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-A - hypot(A, B)) / B));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.9e-147) {
		tmp = (180.0 * Math.atan(((C / B) - (Math.hypot(B, C) / B)))) / Math.PI;
	} else if (C <= 1e+55) {
		tmp = (180.0 / Math.PI) * Math.atan(((-A - Math.hypot(A, B)) / B));
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.9e-147:
		tmp = (180.0 * math.atan(((C / B) - (math.hypot(B, C) / B)))) / math.pi
	elif C <= 1e+55:
		tmp = (180.0 / math.pi) * math.atan(((-A - math.hypot(A, B)) / B))
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.9e-147)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) - Float64(hypot(B, C) / B)))) / pi);
	elseif (C <= 1e+55)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.9e-147)
		tmp = (180.0 * atan(((C / B) - (hypot(B, C) / B)))) / pi;
	elseif (C <= 1e+55)
		tmp = (180.0 / pi) * atan(((-A - hypot(A, B)) / B));
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.9e-147], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] - N[(N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 1e+55], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.9000000000000001e-147

   1. Initial program 67.4%

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

      1. associate-*r/ 67.4%

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

      2. associate-*l/ 67.4%

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

      3. *-un-lft-identity 67.4%

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

      4. unpow2 67.4%

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

      5. unpow2 67.4%

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

      6. hypot-define 91.2%

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

   4. Applied egg-rr 91.2%

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

      1. div-sub 87.8%

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

   6. Applied egg-rr 87.8%

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

   7. Taylor expanded in A around 0 67.4%

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

      1. associate-*l/ 67.4%

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

      2. *-lft-identity 67.4%

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

      3. unpow2 67.4%

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

      4. unpow2 67.4%

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

      5. hypot-define 86.2%

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

   9. Simplified 86.2%

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

   if -2.9000000000000001e-147 < C < 1.00000000000000001e55

   1. Initial program 51.3%

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

   3. Taylor expanded in B around 0 49.6%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in C around 0 50.3%

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

      1. distribute-lft-in 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. mul-1-neg 50.3%

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

      5. unpow2 50.3%

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

      6. unpow2 50.3%

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

      7. hypot-define 74.9%

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

   8. Simplified 74.9%

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

   if 1.00000000000000001e55 < C

   1. Initial program 16.9%

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

      1. associate-*r/ 16.9%

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

      2. associate-*l/ 16.9%

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

      3. *-un-lft-identity 16.9%

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

      4. unpow2 16.9%

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

      5. unpow2 16.9%

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

      6. hypot-define 51.2%

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

   4. Applied egg-rr 51.2%

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

   5. Taylor expanded in C around inf 76.9%

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

   6. Taylor expanded in A around inf 76.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - \frac{\mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{+55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+188}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e+188)
   (* (atan (/ (* B 0.5) A)) (/ 180.0 PI))
   (if (<= A 1.05e+73)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+188) {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((double) M_PI));
	} else if (A <= 1.05e+73) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+188) {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / Math.PI);
	} else if (A <= 1.05e+73) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8e+188:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / math.pi)
	elif A <= 1.05e+73:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8e+188)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / pi));
	elseif (A <= 1.05e+73)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8e+188)
		tmp = atan(((B * 0.5) / A)) * (180.0 / pi);
	elseif (A <= 1.05e+73)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8e+188], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e+73], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.0000000000000002e188

   1. Initial program 5.6%

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

   3. Taylor expanded in A around -inf 91.5%

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

      1. associate-*r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in B around 0 91.5%

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

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-/l* 91.7%

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

      4. associate-*r/ 91.7%

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

      5. *-commutative 91.7%

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

   8. Simplified 91.7%

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

   if -8.0000000000000002e188 < A < 1.0500000000000001e73

   1. Initial program 52.6%

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

   3. Taylor expanded in A around 0 47.5%

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

      1. unpow2 47.5%

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

      2. unpow2 47.5%

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

      3. hypot-define 72.2%

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

   5. Simplified 72.2%

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

   if 1.0500000000000001e73 < A

   1. Initial program 71.8%

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

   3. Taylor expanded in B around -inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. div-sub 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+188}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+188}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{+73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e+188)
   (* (atan (/ (* B 0.5) A)) (/ 180.0 PI))
   (if (<= A 1.22e+73)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+188) {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((double) M_PI));
	} else if (A <= 1.22e+73) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+188) {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / Math.PI);
	} else if (A <= 1.22e+73) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8e+188:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / math.pi)
	elif A <= 1.22e+73:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8e+188)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / pi));
	elseif (A <= 1.22e+73)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8e+188)
		tmp = atan(((B * 0.5) / A)) * (180.0 / pi);
	elseif (A <= 1.22e+73)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8e+188], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.22e+73], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.0000000000000002e188

   1. Initial program 5.6%

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

   3. Taylor expanded in A around -inf 91.5%

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

      1. associate-*r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in B around 0 91.5%

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

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-/l* 91.7%

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

      4. associate-*r/ 91.7%

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

      5. *-commutative 91.7%

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

   8. Simplified 91.7%

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

   if -8.0000000000000002e188 < A < 1.21999999999999998e73

   1. Initial program 52.6%

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

   3. Taylor expanded in B around 0 51.5%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in A around 0 47.5%

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

      1. unpow2 47.5%

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

      2. unpow2 47.5%

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

      3. hypot-define 72.2%

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

   8. Simplified 72.2%

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

   if 1.21999999999999998e73 < A

   1. Initial program 71.8%

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

   3. Taylor expanded in B around -inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. div-sub 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+188}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{+73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{+128}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.9e+128)
   (* (atan (/ (* B 0.5) 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 <= -4.9e+128) {
		tmp = atan(((B * 0.5) / 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 <= -4.9e+128) {
		tmp = Math.atan(((B * 0.5) / 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 <= -4.9e+128:
		tmp = math.atan(((B * 0.5) / 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 <= -4.9e+128)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / 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 <= -4.9e+128)
		tmp = atan(((B * 0.5) / 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, -4.9e+128], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $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 < -4.90000000000000018e128

   1. Initial program 11.2%

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

   3. Taylor expanded in A around -inf 81.3%

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

      1. associate-*r/ 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in B around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. *-commutative 81.3%

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

      3. associate-/l* 81.5%

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

      4. associate-*r/ 81.5%

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

      5. *-commutative 81.5%

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

   8. Simplified 81.5%

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

   if -4.90000000000000018e128 < A

   1. Initial program 58.7%

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

   3. Simplified 80.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{+128}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{+190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.3e+190)
   (* (atan (/ (* B 0.5) 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 <= -4.3e+190) {
		tmp = atan(((B * 0.5) / 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 <= -4.3e+190) {
		tmp = Math.atan(((B * 0.5) / 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 <= -4.3e+190:
		tmp = math.atan(((B * 0.5) / 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 <= -4.3e+190)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / 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 <= -4.3e+190)
		tmp = atan(((B * 0.5) / 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, -4.3e+190], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $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 < -4.3000000000000001e190

   1. Initial program 5.6%

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

   3. Taylor expanded in A around -inf 91.5%

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

      1. associate-*r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in B around 0 91.5%

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

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-/l* 91.7%

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

      4. associate-*r/ 91.7%

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

      5. *-commutative 91.7%

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

   8. Simplified 91.7%

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

   if -4.3000000000000001e190 < A

   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. Step-by-step derivation

      1. associate-*l/ 56.5%

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

      2. *-lft-identity 56.5%

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

      3. +-commutative 56.5%

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

      4. unpow2 56.5%

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

      5. unpow2 56.5%

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

      6. hypot-define 80.5%

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

   3. Simplified 80.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{+190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.26 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-290}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-235}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -1.26e+63)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2e-33)
       t_0
       (if (<= B -1.6e-104)
         t_1
         (if (<= B -2.05e-290)
           t_0
           (if (<= B 4.1e-258)
             t_1
             (if (<= B 1.85e-235)
               t_0
               (if (<= B 1.75e-188)
                 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
                 (if (<= B 8e-37) 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 t_1 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.26e+63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2e-33) {
		tmp = t_0;
	} else if (B <= -1.6e-104) {
		tmp = t_1;
	} else if (B <= -2.05e-290) {
		tmp = t_0;
	} else if (B <= 4.1e-258) {
		tmp = t_1;
	} else if (B <= 1.85e-235) {
		tmp = t_0;
	} else if (B <= 1.75e-188) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 8e-37) {
		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 t_1 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -1.26e+63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2e-33) {
		tmp = t_0;
	} else if (B <= -1.6e-104) {
		tmp = t_1;
	} else if (B <= -2.05e-290) {
		tmp = t_0;
	} else if (B <= 4.1e-258) {
		tmp = t_1;
	} else if (B <= 1.85e-235) {
		tmp = t_0;
	} else if (B <= 1.75e-188) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 8e-37) {
		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)
	t_1 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -1.26e+63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2e-33:
		tmp = t_0
	elif B <= -1.6e-104:
		tmp = t_1
	elif B <= -2.05e-290:
		tmp = t_0
	elif B <= 4.1e-258:
		tmp = t_1
	elif B <= 1.85e-235:
		tmp = t_0
	elif B <= 1.75e-188:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 8e-37:
		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))
	t_1 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -1.26e+63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2e-33)
		tmp = t_0;
	elseif (B <= -1.6e-104)
		tmp = t_1;
	elseif (B <= -2.05e-290)
		tmp = t_0;
	elseif (B <= 4.1e-258)
		tmp = t_1;
	elseif (B <= 1.85e-235)
		tmp = t_0;
	elseif (B <= 1.75e-188)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 8e-37)
		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);
	t_1 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -1.26e+63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2e-33)
		tmp = t_0;
	elseif (B <= -1.6e-104)
		tmp = t_1;
	elseif (B <= -2.05e-290)
		tmp = t_0;
	elseif (B <= 4.1e-258)
		tmp = t_1;
	elseif (B <= 1.85e-235)
		tmp = t_0;
	elseif (B <= 1.75e-188)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 8e-37)
		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]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.26e+63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-33], t$95$0, If[LessEqual[B, -1.6e-104], t$95$1, If[LessEqual[B, -2.05e-290], t$95$0, If[LessEqual[B, 4.1e-258], t$95$1, If[LessEqual[B, 1.85e-235], t$95$0, If[LessEqual[B, 1.75e-188], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8e-37], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.26e63

   1. Initial program 38.9%

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

   3. Taylor expanded in B around -inf 76.8%

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

   if -1.26e63 < B < -2.0000000000000001e-33 or -1.59999999999999994e-104 < B < -2.0500000000000001e-290 or 4.1000000000000001e-258 < B < 1.8500000000000001e-235 or 1.75e-188 < B < 8.00000000000000053e-37

   1. Initial program 44.8%

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

      1. associate-*r/ 44.8%

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

      2. associate-*l/ 44.8%

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

      3. *-un-lft-identity 44.8%

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

      4. unpow2 44.8%

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

      5. unpow2 44.8%

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

      6. hypot-define 63.0%

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

   4. Applied egg-rr 63.0%

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

   5. Taylor expanded in C around inf 44.2%

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

   6. Taylor expanded in A around inf 44.2%

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

   if -2.0000000000000001e-33 < B < -1.59999999999999994e-104 or -2.0500000000000001e-290 < B < 4.1000000000000001e-258

   1. Initial program 78.7%

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

   3. Taylor expanded in B around inf 63.5%

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

   4. Taylor expanded in C around inf 60.5%

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

   if 1.8500000000000001e-235 < B < 1.75e-188

   1. Initial program 62.7%

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

   3. Taylor expanded in A around inf 51.2%

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

   if 8.00000000000000053e-37 < B

   1. Initial program 52.3%

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

   3. Taylor expanded in B around inf 64.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.26 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.46 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-236}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6.9 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -1.46e+63)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1.6e-33)
       t_0
       (if (<= B -3.7e-103)
         (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
         (if (<= B -7.4e-292)
           t_0
           (if (<= B 4.3e-259)
             (* 180.0 (/ (atan (/ C B)) PI))
             (if (<= B 9.2e-236)
               t_0
               (if (<= B 6.9e-187)
                 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
                 (if (<= B 1.4e-33) 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 <= -1.46e+63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.6e-33) {
		tmp = t_0;
	} else if (B <= -3.7e-103) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= -7.4e-292) {
		tmp = t_0;
	} else if (B <= 4.3e-259) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 9.2e-236) {
		tmp = t_0;
	} else if (B <= 6.9e-187) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 1.4e-33) {
		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 <= -1.46e+63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.6e-33) {
		tmp = t_0;
	} else if (B <= -3.7e-103) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= -7.4e-292) {
		tmp = t_0;
	} else if (B <= 4.3e-259) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 9.2e-236) {
		tmp = t_0;
	} else if (B <= 6.9e-187) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 1.4e-33) {
		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 <= -1.46e+63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.6e-33:
		tmp = t_0
	elif B <= -3.7e-103:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= -7.4e-292:
		tmp = t_0
	elif B <= 4.3e-259:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 9.2e-236:
		tmp = t_0
	elif B <= 6.9e-187:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 1.4e-33:
		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 <= -1.46e+63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.6e-33)
		tmp = t_0;
	elseif (B <= -3.7e-103)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= -7.4e-292)
		tmp = t_0;
	elseif (B <= 4.3e-259)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 9.2e-236)
		tmp = t_0;
	elseif (B <= 6.9e-187)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 1.4e-33)
		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 <= -1.46e+63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.6e-33)
		tmp = t_0;
	elseif (B <= -3.7e-103)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= -7.4e-292)
		tmp = t_0;
	elseif (B <= 4.3e-259)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 9.2e-236)
		tmp = t_0;
	elseif (B <= 6.9e-187)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 1.4e-33)
		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, -1.46e+63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.6e-33], t$95$0, If[LessEqual[B, -3.7e-103], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.4e-292], t$95$0, If[LessEqual[B, 4.3e-259], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.2e-236], t$95$0, If[LessEqual[B, 6.9e-187], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-33], 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 < -1.4599999999999999e63

   1. Initial program 38.9%

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

   3. Taylor expanded in B around -inf 76.8%

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

   if -1.4599999999999999e63 < B < -1.59999999999999988e-33 or -3.6999999999999999e-103 < B < -7.39999999999999993e-292 or 4.3000000000000001e-259 < B < 9.20000000000000024e-236 or 6.90000000000000045e-187 < B < 1.4e-33

   1. Initial program 44.8%

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

      1. associate-*r/ 44.8%

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

      2. associate-*l/ 44.8%

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

      3. *-un-lft-identity 44.8%

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

      4. unpow2 44.8%

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

      5. unpow2 44.8%

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

      6. hypot-define 63.0%

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

   4. Applied egg-rr 63.0%

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

   5. Taylor expanded in C around inf 44.2%

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

   6. Taylor expanded in A around inf 44.2%

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

   if -1.59999999999999988e-33 < B < -3.6999999999999999e-103

   1. Initial program 83.0%

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

   3. Taylor expanded in C around -inf 54.3%

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

   if -7.39999999999999993e-292 < B < 4.3000000000000001e-259

   1. Initial program 71.4%

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

   3. Taylor expanded in B around inf 60.3%

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

   4. Taylor expanded in C around inf 71.0%

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

   if 9.20000000000000024e-236 < B < 6.90000000000000045e-187

   1. Initial program 62.7%

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

   3. Taylor expanded in A around inf 51.2%

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

   if 1.4e-33 < B

   1. Initial program 52.3%

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

   3. Taylor expanded in B around inf 64.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.46 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.9 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t\_1\right)}{\pi}\\ \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-272}:\\ \;\;\;\;t\_0 \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (* B 0.5) A)))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -1.42e+66)
     t_2
     (if (<= B -7.2e+27)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -9.5e-193)
         t_2
         (if (<= B -8.8e-222)
           (* 180.0 (/ t_0 PI))
           (if (<= B -2e-269)
             t_2
             (if (<= B 2.6e-272)
               (* t_0 (/ 180.0 PI))
               (/ (* 180.0 (atan (+ t_1 -1.0))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((B * 0.5) / A));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -1.42e+66) {
		tmp = t_2;
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -9.5e-193) {
		tmp = t_2;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (B <= -2e-269) {
		tmp = t_2;
	} else if (B <= 2.6e-272) {
		tmp = t_0 * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_1 + -1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((B * 0.5) / A));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -1.42e+66) {
		tmp = t_2;
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -9.5e-193) {
		tmp = t_2;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (B <= -2e-269) {
		tmp = t_2;
	} else if (B <= 2.6e-272) {
		tmp = t_0 * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((t_1 + -1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((B * 0.5) / A))
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -1.42e+66:
		tmp = t_2
	elif B <= -7.2e+27:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -9.5e-193:
		tmp = t_2
	elif B <= -8.8e-222:
		tmp = 180.0 * (t_0 / math.pi)
	elif B <= -2e-269:
		tmp = t_2
	elif B <= 2.6e-272:
		tmp = t_0 * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((t_1 + -1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(B * 0.5) / A))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -1.42e+66)
		tmp = t_2;
	elseif (B <= -7.2e+27)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -9.5e-193)
		tmp = t_2;
	elseif (B <= -8.8e-222)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (B <= -2e-269)
		tmp = t_2;
	elseif (B <= 2.6e-272)
		tmp = Float64(t_0 * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(t_1 + -1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((B * 0.5) / A));
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -1.42e+66)
		tmp = t_2;
	elseif (B <= -7.2e+27)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -9.5e-193)
		tmp = t_2;
	elseif (B <= -8.8e-222)
		tmp = 180.0 * (t_0 / pi);
	elseif (B <= -2e-269)
		tmp = t_2;
	elseif (B <= 2.6e-272)
		tmp = t_0 * (180.0 / pi);
	else
		tmp = (180.0 * atan((t_1 + -1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.42e+66], t$95$2, If[LessEqual[B, -7.2e+27], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-193], t$95$2, If[LessEqual[B, -8.8e-222], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-269], t$95$2, If[LessEqual[B, 2.6e-272], N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.4200000000000001e66 or -7.19999999999999966e27 < B < -9.5000000000000003e-193 or -8.8000000000000001e-222 < B < -1.9999999999999999e-269

   1. Initial program 53.1%

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

   3. Taylor expanded in B around -inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   if -1.4200000000000001e66 < B < -7.19999999999999966e27

   1. Initial program 13.7%

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

      1. associate-*r/ 13.7%

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

      2. associate-*l/ 13.7%

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

      3. *-un-lft-identity 13.7%

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

      4. unpow2 13.7%

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

      5. unpow2 13.7%

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

      6. hypot-define 14.5%

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

   4. Applied egg-rr 14.5%

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

   5. Taylor expanded in C around inf 52.9%

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

   6. Taylor expanded in A around inf 53.0%

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

   if -9.5000000000000003e-193 < B < -8.8000000000000001e-222

   1. Initial program 5.7%

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

   3. Taylor expanded in A around -inf 88.4%

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

      1. associate-*r/ 88.4%

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

   5. Simplified 88.4%

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

   if -1.9999999999999999e-269 < B < 2.59999999999999992e-272

   1. Initial program 48.1%

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

   3. Taylor expanded in A around -inf 70.5%

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

      1. associate-*r/ 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in B around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-/l* 70.6%

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

      4. associate-*r/ 70.6%

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

      5. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if 2.59999999999999992e-272 < B

   1. Initial program 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*l/ 53.5%

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

      3. *-un-lft-identity 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. +-commutative 65.1%

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

      3. distribute-neg-in 65.1%

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

      4. metadata-eval 65.1%

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

      5. mul-1-neg 65.1%

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

      6. associate-+l+ 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. sub-neg 65.1%

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

      10. div-sub 66.7%

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

   7. Simplified 66.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-272}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ t_1 := \frac{C - A}{B}\\ t_2 := \tan^{-1} \left(1 + t\_1\right)\\ t_3 := 180 \cdot \frac{t\_2}{\pi}\\ \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;\frac{180 \cdot t\_2}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-268}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-273}:\\ \;\;\;\;t\_0 \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (* B 0.5) A)))
        (t_1 (/ (- C A) B))
        (t_2 (atan (+ 1.0 t_1)))
        (t_3 (* 180.0 (/ t_2 PI))))
   (if (<= B -1.42e+66)
     (/ (* 180.0 t_2) PI)
     (if (<= B -7.2e+27)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -2.7e-191)
         t_3
         (if (<= B -8.8e-222)
           (* 180.0 (/ t_0 PI))
           (if (<= B -1.02e-268)
             t_3
             (if (<= B 9e-273)
               (* t_0 (/ 180.0 PI))
               (/ (* 180.0 (atan (+ t_1 -1.0))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((B * 0.5) / A));
	double t_1 = (C - A) / B;
	double t_2 = atan((1.0 + t_1));
	double t_3 = 180.0 * (t_2 / ((double) M_PI));
	double tmp;
	if (B <= -1.42e+66) {
		tmp = (180.0 * t_2) / ((double) M_PI);
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -2.7e-191) {
		tmp = t_3;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (B <= -1.02e-268) {
		tmp = t_3;
	} else if (B <= 9e-273) {
		tmp = t_0 * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_1 + -1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((B * 0.5) / A));
	double t_1 = (C - A) / B;
	double t_2 = Math.atan((1.0 + t_1));
	double t_3 = 180.0 * (t_2 / Math.PI);
	double tmp;
	if (B <= -1.42e+66) {
		tmp = (180.0 * t_2) / Math.PI;
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -2.7e-191) {
		tmp = t_3;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (B <= -1.02e-268) {
		tmp = t_3;
	} else if (B <= 9e-273) {
		tmp = t_0 * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((t_1 + -1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((B * 0.5) / A))
	t_1 = (C - A) / B
	t_2 = math.atan((1.0 + t_1))
	t_3 = 180.0 * (t_2 / math.pi)
	tmp = 0
	if B <= -1.42e+66:
		tmp = (180.0 * t_2) / math.pi
	elif B <= -7.2e+27:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -2.7e-191:
		tmp = t_3
	elif B <= -8.8e-222:
		tmp = 180.0 * (t_0 / math.pi)
	elif B <= -1.02e-268:
		tmp = t_3
	elif B <= 9e-273:
		tmp = t_0 * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((t_1 + -1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(B * 0.5) / A))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = atan(Float64(1.0 + t_1))
	t_3 = Float64(180.0 * Float64(t_2 / pi))
	tmp = 0.0
	if (B <= -1.42e+66)
		tmp = Float64(Float64(180.0 * t_2) / pi);
	elseif (B <= -7.2e+27)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -2.7e-191)
		tmp = t_3;
	elseif (B <= -8.8e-222)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (B <= -1.02e-268)
		tmp = t_3;
	elseif (B <= 9e-273)
		tmp = Float64(t_0 * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(t_1 + -1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((B * 0.5) / A));
	t_1 = (C - A) / B;
	t_2 = atan((1.0 + t_1));
	t_3 = 180.0 * (t_2 / pi);
	tmp = 0.0;
	if (B <= -1.42e+66)
		tmp = (180.0 * t_2) / pi;
	elseif (B <= -7.2e+27)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -2.7e-191)
		tmp = t_3;
	elseif (B <= -8.8e-222)
		tmp = 180.0 * (t_0 / pi);
	elseif (B <= -1.02e-268)
		tmp = t_3;
	elseif (B <= 9e-273)
		tmp = t_0 * (180.0 / pi);
	else
		tmp = (180.0 * atan((t_1 + -1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(180.0 * N[(t$95$2 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.42e+66], N[(N[(180.0 * t$95$2), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -7.2e+27], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.7e-191], t$95$3, If[LessEqual[B, -8.8e-222], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.02e-268], t$95$3, If[LessEqual[B, 9e-273], N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.4200000000000001e66

   1. Initial program 39.6%

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

      1. associate-*r/ 39.6%

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

      2. associate-*l/ 39.6%

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

      3. *-un-lft-identity 39.6%

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

      4. unpow2 39.6%

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

      5. unpow2 39.6%

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

      6. hypot-define 84.9%

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

   4. Applied egg-rr 84.9%

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

   5. Taylor expanded in B around -inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. div-sub 81.6%

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

   7. Simplified 81.6%

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

   if -1.4200000000000001e66 < B < -7.19999999999999966e27

   1. Initial program 13.7%

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

      1. associate-*r/ 13.7%

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

      2. associate-*l/ 13.7%

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

      3. *-un-lft-identity 13.7%

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

      4. unpow2 13.7%

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

      5. unpow2 13.7%

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

      6. hypot-define 14.5%

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

   4. Applied egg-rr 14.5%

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

   5. Taylor expanded in C around inf 52.9%

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

   6. Taylor expanded in A around inf 53.0%

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

   if -7.19999999999999966e27 < B < -2.69999999999999999e-191 or -8.8000000000000001e-222 < B < -1.0200000000000001e-268

   1. Initial program 65.2%

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

   3. Taylor expanded in B around -inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. div-sub 63.5%

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

   5. Simplified 63.5%

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

   if -2.69999999999999999e-191 < B < -8.8000000000000001e-222

   1. Initial program 5.7%

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

   3. Taylor expanded in A around -inf 88.4%

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

      1. associate-*r/ 88.4%

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

   5. Simplified 88.4%

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

   if -1.0200000000000001e-268 < B < 8.99999999999999921e-273

   1. Initial program 48.1%

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

   3. Taylor expanded in A around -inf 70.5%

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

      1. associate-*r/ 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in B around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-/l* 70.6%

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

      4. associate-*r/ 70.6%

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

      5. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if 8.99999999999999921e-273 < B

   1. Initial program 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*l/ 53.5%

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

      3. *-un-lft-identity 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. +-commutative 65.1%

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

      3. distribute-neg-in 65.1%

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

      4. metadata-eval 65.1%

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

      5. mul-1-neg 65.1%

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

      6. associate-+l+ 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. sub-neg 65.1%

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

      10. div-sub 66.7%

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

   7. Simplified 66.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 + \frac{C - A}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-273}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \tan^{-1} \left(1 + t\_0\right)\\ t_2 := 180 \cdot \frac{t\_1}{\pi}\\ \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;\frac{180 \cdot t\_1}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{-A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-272}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B))
        (t_1 (atan (+ 1.0 t_0)))
        (t_2 (* 180.0 (/ t_1 PI))))
   (if (<= B -1.42e+66)
     (/ (* 180.0 t_1) PI)
     (if (<= B -7.2e+27)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -4.6e-189)
         t_2
         (if (<= B -8.8e-222)
           (* 180.0 (/ (atan (/ (* -0.5 (+ B (* B (/ C A)))) (- A))) PI))
           (if (<= B -6.2e-267)
             t_2
             (if (<= B 2.5e-272)
               (* (atan (/ (* B 0.5) A)) (/ 180.0 PI))
               (/ (* 180.0 (atan (+ t_0 -1.0))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = atan((1.0 + t_0));
	double t_2 = 180.0 * (t_1 / ((double) M_PI));
	double tmp;
	if (B <= -1.42e+66) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -4.6e-189) {
		tmp = t_2;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (atan(((-0.5 * (B + (B * (C / A)))) / -A)) / ((double) M_PI));
	} else if (B <= -6.2e-267) {
		tmp = t_2;
	} else if (B <= 2.5e-272) {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_0 + -1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = Math.atan((1.0 + t_0));
	double t_2 = 180.0 * (t_1 / Math.PI);
	double tmp;
	if (B <= -1.42e+66) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (B <= -7.2e+27) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -4.6e-189) {
		tmp = t_2;
	} else if (B <= -8.8e-222) {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + (B * (C / A)))) / -A)) / Math.PI);
	} else if (B <= -6.2e-267) {
		tmp = t_2;
	} else if (B <= 2.5e-272) {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((t_0 + -1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = math.atan((1.0 + t_0))
	t_2 = 180.0 * (t_1 / math.pi)
	tmp = 0
	if B <= -1.42e+66:
		tmp = (180.0 * t_1) / math.pi
	elif B <= -7.2e+27:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -4.6e-189:
		tmp = t_2
	elif B <= -8.8e-222:
		tmp = 180.0 * (math.atan(((-0.5 * (B + (B * (C / A)))) / -A)) / math.pi)
	elif B <= -6.2e-267:
		tmp = t_2
	elif B <= 2.5e-272:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((t_0 + -1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = atan(Float64(1.0 + t_0))
	t_2 = Float64(180.0 * Float64(t_1 / pi))
	tmp = 0.0
	if (B <= -1.42e+66)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (B <= -7.2e+27)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -4.6e-189)
		tmp = t_2;
	elseif (B <= -8.8e-222)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(B * Float64(C / A)))) / Float64(-A))) / pi));
	elseif (B <= -6.2e-267)
		tmp = t_2;
	elseif (B <= 2.5e-272)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + -1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	t_1 = atan((1.0 + t_0));
	t_2 = 180.0 * (t_1 / pi);
	tmp = 0.0;
	if (B <= -1.42e+66)
		tmp = (180.0 * t_1) / pi;
	elseif (B <= -7.2e+27)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -4.6e-189)
		tmp = t_2;
	elseif (B <= -8.8e-222)
		tmp = 180.0 * (atan(((-0.5 * (B + (B * (C / A)))) / -A)) / pi);
	elseif (B <= -6.2e-267)
		tmp = t_2;
	elseif (B <= 2.5e-272)
		tmp = atan(((B * 0.5) / A)) * (180.0 / pi);
	else
		tmp = (180.0 * atan((t_0 + -1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.42e+66], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -7.2e+27], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.6e-189], t$95$2, If[LessEqual[B, -8.8e-222], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.2e-267], t$95$2, If[LessEqual[B, 2.5e-272], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.4200000000000001e66

   1. Initial program 39.6%

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

      1. associate-*r/ 39.6%

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

      2. associate-*l/ 39.6%

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

      3. *-un-lft-identity 39.6%

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

      4. unpow2 39.6%

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

      5. unpow2 39.6%

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

      6. hypot-define 84.9%

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

   4. Applied egg-rr 84.9%

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

   5. Taylor expanded in B around -inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. div-sub 81.6%

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

   7. Simplified 81.6%

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

   if -1.4200000000000001e66 < B < -7.19999999999999966e27

   1. Initial program 13.7%

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

      1. associate-*r/ 13.7%

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

      2. associate-*l/ 13.7%

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

      3. *-un-lft-identity 13.7%

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

      4. unpow2 13.7%

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

      5. unpow2 13.7%

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

      6. hypot-define 14.5%

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

   4. Applied egg-rr 14.5%

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

   5. Taylor expanded in C around inf 52.9%

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

   6. Taylor expanded in A around inf 53.0%

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

   if -7.19999999999999966e27 < B < -4.5999999999999996e-189 or -8.8000000000000001e-222 < B < -6.2000000000000002e-267

   1. Initial program 64.5%

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

   3. Taylor expanded in B around -inf 61.0%

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

      1. associate--l+ 61.0%

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

      2. div-sub 62.8%

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

   5. Simplified 62.8%

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

   if -4.5999999999999996e-189 < B < -8.8000000000000001e-222

   1. Initial program 17.5%

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

   3. Taylor expanded in A around -inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-neg-frac2 89.8%

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

      3. distribute-lft-out 89.8%

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

      4. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

   if -6.2000000000000002e-267 < B < 2.49999999999999991e-272

   1. Initial program 48.1%

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

   3. Taylor expanded in A around -inf 70.5%

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

      1. associate-*r/ 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in B around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-/l* 70.6%

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

      4. associate-*r/ 70.6%

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

      5. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if 2.49999999999999991e-272 < B

   1. Initial program 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*l/ 53.5%

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

      3. *-un-lft-identity 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. +-commutative 65.1%

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

      3. distribute-neg-in 65.1%

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

      4. metadata-eval 65.1%

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

      5. mul-1-neg 65.1%

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

      6. associate-+l+ 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. sub-neg 65.1%

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

      10. div-sub 66.7%

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

   7. Simplified 66.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 + \frac{C - A}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.6 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{-A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-267}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-272}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.12 \cdot 10^{+32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -9.5 \cdot 10^{-206}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-282}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))
   (if (<= C -1.12e+32)
     (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
     (if (<= C -9.5e-206)
       t_0
       (if (<= C -7e-282)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= C 4.1e-5) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

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 <= -1.12e+32) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (C <= -9.5e-206) {
		tmp = t_0;
	} else if (C <= -7e-282) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 4.1e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.12e+32) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (C <= -9.5e-206) {
		tmp = t_0;
	} else if (C <= -7e-282) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 4.1e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.12e+32:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif C <= -9.5e-206:
		tmp = t_0
	elif C <= -7e-282:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 4.1e-5:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.12e+32)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (C <= -9.5e-206)
		tmp = t_0;
	elseif (C <= -7e-282)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 4.1e-5)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	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 <= -1.12e+32)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (C <= -9.5e-206)
		tmp = t_0;
	elseif (C <= -7e-282)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 4.1e-5)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / 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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.12e+32], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -9.5e-206], t$95$0, If[LessEqual[C, -7e-282], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.1e-5], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.12000000000000007e32

   1. Initial program 74.6%

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

   3. Taylor expanded in C around -inf 68.9%

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

   if -1.12000000000000007e32 < C < -9.49999999999999979e-206 or -7.00000000000000013e-282 < C < 4.10000000000000005e-5

   1. Initial program 58.8%

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

   3. Taylor expanded in B around inf 51.9%

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

   4. Taylor expanded in C around 0 49.8%

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

      1. neg-mul-1 49.8%

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

      2. distribute-neg-in 49.8%

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

      3. metadata-eval 49.8%

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

      4. unsub-neg 49.8%

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

   6. Simplified 49.8%

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

   if -9.49999999999999979e-206 < C < -7.00000000000000013e-282

   1. Initial program 18.9%

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

   3. Taylor expanded in B around -inf 46.1%

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

   if 4.10000000000000005e-5 < C

   1. Initial program 20.3%

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

      1. associate-*r/ 20.3%

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

      2. associate-*l/ 20.3%

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

      3. *-un-lft-identity 20.3%

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

      4. unpow2 20.3%

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

      5. unpow2 20.3%

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

      6. hypot-define 49.3%

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

   4. Applied egg-rr 49.3%

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

   5. Taylor expanded in C around inf 66.9%

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

   6. Taylor expanded in A around inf 66.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.12 \cdot 10^{+32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -9.5 \cdot 10^{-206}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-282}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -2.5e+19)
     (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
     (if (<= C 3.5e-140)
       t_0
       (if (<= C 3.3e-67)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 2.4e-5) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

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 <= -2.5e+19) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (C <= 3.5e-140) {
		tmp = t_0;
	} else if (C <= 3.3e-67) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 2.4e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -2.5e+19) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (C <= 3.5e-140) {
		tmp = t_0;
	} else if (C <= 3.3e-67) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 2.4e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -2.5e+19:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif C <= 3.5e-140:
		tmp = t_0
	elif C <= 3.3e-67:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 2.4e-5:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -2.5e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (C <= 3.5e-140)
		tmp = t_0;
	elseif (C <= 3.3e-67)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 2.4e-5)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	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 <= -2.5e+19)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (C <= 3.5e-140)
		tmp = t_0;
	elseif (C <= 3.3e-67)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 2.4e-5)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / 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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -2.5e+19], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.5e-140], t$95$0, If[LessEqual[C, 3.3e-67], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.4e-5], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -2.5e19

   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 67.6%

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

   if -2.5e19 < C < 3.4999999999999998e-140 or 3.3000000000000002e-67 < C < 2.4000000000000001e-5

   1. Initial program 56.9%

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

   3. Taylor expanded in C around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-neg-frac2 54.5%

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

      3. +-commutative 54.5%

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

      4. unpow2 54.5%

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

      5. unpow2 54.5%

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

      6. hypot-define 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in B around -inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. sub-neg 55.1%

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

   8. Simplified 55.1%

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

   if 3.4999999999999998e-140 < C < 3.3000000000000002e-67

   1. Initial program 38.0%

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

   3. Taylor expanded in B around inf 49.1%

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

   if 2.4000000000000001e-5 < C

   1. Initial program 20.3%

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

      1. associate-*r/ 20.3%

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

      2. associate-*l/ 20.3%

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

      3. *-un-lft-identity 20.3%

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

      4. unpow2 20.3%

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

      5. unpow2 20.3%

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

      6. hypot-define 49.3%

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

   4. Applied egg-rr 49.3%

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

   5. Taylor expanded in C around inf 66.9%

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

   6. Taylor expanded in A around inf 66.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.65 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -4.8e-148)
     (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
     (if (<= C 1.65e-140)
       t_0
       (if (<= C 6.4e-65)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 3.2e-5) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

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 <= -4.8e-148) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 1.65e-140) {
		tmp = t_0;
	} else if (C <= 6.4e-65) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 3.2e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -4.8e-148) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 1.65e-140) {
		tmp = t_0;
	} else if (C <= 6.4e-65) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 3.2e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -4.8e-148:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 1.65e-140:
		tmp = t_0
	elif C <= 6.4e-65:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 3.2e-5:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -4.8e-148)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 1.65e-140)
		tmp = t_0;
	elseif (C <= 6.4e-65)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 3.2e-5)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	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 <= -4.8e-148)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 1.65e-140)
		tmp = t_0;
	elseif (C <= 6.4e-65)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 3.2e-5)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / 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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -4.8e-148], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.65e-140], t$95$0, If[LessEqual[C, 6.4e-65], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.2e-5], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.8000000000000002e-148

   1. Initial program 67.4%

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

   3. Taylor expanded in B around inf 68.8%

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

   4. Taylor expanded in A around 0 70.3%

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

   if -4.8000000000000002e-148 < C < 1.64999999999999994e-140 or 6.3999999999999998e-65 < C < 3.19999999999999986e-5

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-neg-frac2 56.3%

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

      3. +-commutative 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-define 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in B around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. sub-neg 59.4%

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

   8. Simplified 59.4%

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

   if 1.64999999999999994e-140 < C < 6.3999999999999998e-65

   1. Initial program 38.0%

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

   3. Taylor expanded in B around inf 49.1%

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

   if 3.19999999999999986e-5 < C

   1. Initial program 20.3%

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

      1. associate-*r/ 20.3%

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

      2. associate-*l/ 20.3%

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

      3. *-un-lft-identity 20.3%

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

      4. unpow2 20.3%

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

      5. unpow2 20.3%

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

      6. hypot-define 49.3%

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

   4. Applied egg-rr 49.3%

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

   5. Taylor expanded in C around inf 66.9%

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

   6. Taylor expanded in A around inf 66.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.65 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.55 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -1.5e-147)
     (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)
     (if (<= C 3.55e-140)
       t_0
       (if (<= C 3.8e-67)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 3.5e-5) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

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 <= -1.5e-147) {
		tmp = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	} else if (C <= 3.55e-140) {
		tmp = t_0;
	} else if (C <= 3.8e-67) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 3.5e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.5e-147) {
		tmp = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	} else if (C <= 3.55e-140) {
		tmp = t_0;
	} else if (C <= 3.8e-67) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 3.5e-5) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.5e-147:
		tmp = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	elif C <= 3.55e-140:
		tmp = t_0
	elif C <= 3.8e-67:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 3.5e-5:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.5e-147)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi);
	elseif (C <= 3.55e-140)
		tmp = t_0;
	elseif (C <= 3.8e-67)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 3.5e-5)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	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 <= -1.5e-147)
		tmp = (180.0 * atan(((C / B) + -1.0))) / pi;
	elseif (C <= 3.55e-140)
		tmp = t_0;
	elseif (C <= 3.8e-67)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 3.5e-5)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / 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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.5e-147], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 3.55e-140], t$95$0, If[LessEqual[C, 3.8e-67], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.5e-5], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.5000000000000001e-147

   1. Initial program 67.4%

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

      1. associate-*r/ 67.4%

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

      2. associate-*l/ 67.4%

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

      3. *-un-lft-identity 67.4%

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

      4. unpow2 67.4%

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

      5. unpow2 67.4%

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

      6. hypot-define 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in B around inf 68.8%

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

      1. sub-neg 68.8%

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

      2. +-commutative 68.8%

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

      3. distribute-neg-in 68.8%

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

      4. metadata-eval 68.8%

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

      5. mul-1-neg 68.8%

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

      6. associate-+l+ 68.8%

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

      7. +-commutative 68.8%

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

      8. mul-1-neg 68.8%

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

      9. sub-neg 68.8%

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

      10. div-sub 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in C around inf 70.3%

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

   if -1.5000000000000001e-147 < C < 3.54999999999999993e-140 or 3.79999999999999988e-67 < C < 3.4999999999999997e-5

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-neg-frac2 56.3%

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

      3. +-commutative 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-define 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in B around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. sub-neg 59.4%

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

   8. Simplified 59.4%

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

   if 3.54999999999999993e-140 < C < 3.79999999999999988e-67

   1. Initial program 38.0%

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

   3. Taylor expanded in B around inf 49.1%

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

   if 3.4999999999999997e-5 < C

   1. Initial program 20.3%

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

      1. associate-*r/ 20.3%

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

      2. associate-*l/ 20.3%

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

      3. *-un-lft-identity 20.3%

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

      4. unpow2 20.3%

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

      5. unpow2 20.3%

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

      6. hypot-define 49.3%

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

   4. Applied egg-rr 49.3%

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

   5. Taylor expanded in C around inf 66.9%

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

   6. Taylor expanded in A around inf 66.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.55 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-258}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -1.45e-58)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 6e-258)
       t_0
       (if (<= B 1.9e-81)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 1.85e-13) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.45e-58) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6e-258) {
		tmp = t_0;
	} else if (B <= 1.9e-81) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 1.85e-13) {
		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((C / B)) / Math.PI);
	double tmp;
	if (B <= -1.45e-58) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6e-258) {
		tmp = t_0;
	} else if (B <= 1.9e-81) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 1.85e-13) {
		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((C / B)) / math.pi)
	tmp = 0
	if B <= -1.45e-58:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6e-258:
		tmp = t_0
	elif B <= 1.9e-81:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 1.85e-13:
		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(C / B)) / pi))
	tmp = 0.0
	if (B <= -1.45e-58)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6e-258)
		tmp = t_0;
	elseif (B <= 1.9e-81)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 1.85e-13)
		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((C / B)) / pi);
	tmp = 0.0;
	if (B <= -1.45e-58)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6e-258)
		tmp = t_0;
	elseif (B <= 1.9e-81)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 1.85e-13)
		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[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.45e-58], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6e-258], t$95$0, If[LessEqual[B, 1.9e-81], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.85e-13], 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 < -1.44999999999999995e-58

   1. Initial program 40.9%

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

   3. Taylor expanded in B around -inf 57.7%

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

   if -1.44999999999999995e-58 < B < 6.00000000000000042e-258 or 1.8999999999999999e-81 < B < 1.84999999999999994e-13

   1. Initial program 62.5%

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

   3. Taylor expanded in B around inf 52.9%

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

   4. Taylor expanded in C around inf 41.9%

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

   if 6.00000000000000042e-258 < B < 1.8999999999999999e-81

   1. Initial program 50.2%

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

      1. associate-*r/ 50.2%

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

      2. associate-*l/ 50.2%

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

      3. *-un-lft-identity 50.2%

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

      4. unpow2 50.2%

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

      5. unpow2 50.2%

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

      6. hypot-define 74.4%

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

   4. Applied egg-rr 74.4%

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

      1. div-sub 47.7%

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

   6. Applied egg-rr 47.7%

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

   7. Taylor expanded in C around inf 9.5%

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

      1. distribute-lft1-in 9.5%

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

      2. metadata-eval 9.5%

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

      3. mul0-lft 29.5%

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

      4. metadata-eval 29.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   9. Simplified 29.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   if 1.84999999999999994e-13 < B

   1. Initial program 47.3%

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

   3. Taylor expanded in B around inf 66.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-59)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.16e-263)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 3.8e-32)
       (* 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 <= -1e-59) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.16e-263) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 3.8e-32) {
		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 <= -1e-59) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.16e-263) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 3.8e-32) {
		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 <= -1e-59:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.16e-263:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 3.8e-32:
		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 <= -1e-59)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.16e-263)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 3.8e-32)
		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 <= -1e-59)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.16e-263)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 3.8e-32)
		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, -1e-59], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.16e-263], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-32], 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 < -1e-59

   1. Initial program 40.9%

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

   3. Taylor expanded in B around -inf 57.7%

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

   if -1e-59 < B < 1.1599999999999999e-263

   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. Taylor expanded in B around inf 49.2%

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

   4. Taylor expanded in C around inf 39.9%

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

   if 1.1599999999999999e-263 < B < 3.80000000000000008e-32

   1. Initial program 52.3%

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

   3. Taylor expanded in A around inf 35.9%

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

   if 3.80000000000000008e-32 < B

   1. Initial program 51.5%

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

   3. Taylor expanded in B around inf 65.6%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-263}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 59.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2e-140)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= C 3.3e-67)
     (* 180.0 (/ (atan -1.0) PI))
     (if (<= C 2.6e-5)
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2e-140) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (C <= 3.3e-67) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 2.6e-5) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2e-140) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (C <= 3.3e-67) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 2.6e-5) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2e-140:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif C <= 3.3e-67:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 2.6e-5:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2e-140)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (C <= 3.3e-67)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 2.6e-5)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2e-140)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (C <= 3.3e-67)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 2.6e-5)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2e-140], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.3e-67], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.6e-5], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < 2e-140

   1. Initial program 63.0%

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

   3. Taylor expanded in B around -inf 62.2%

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

      1. associate--l+ 62.2%

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

      2. div-sub 63.4%

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

   5. Simplified 63.4%

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

   if 2e-140 < C < 3.3000000000000002e-67

   1. Initial program 38.0%

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

   3. Taylor expanded in B around inf 49.1%

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

   if 3.3000000000000002e-67 < C < 2.59999999999999984e-5

   1. Initial program 45.4%

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

   3. Taylor expanded in C around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-neg-frac2 45.4%

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

      3. +-commutative 45.4%

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

      4. unpow2 45.4%

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

      5. unpow2 45.4%

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

      6. hypot-define 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in B around -inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. sub-neg 55.1%

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

   8. Simplified 55.1%

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

   if 2.59999999999999984e-5 < C

   1. Initial program 20.3%

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

      1. associate-*r/ 20.3%

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

      2. associate-*l/ 20.3%

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

      3. *-un-lft-identity 20.3%

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

      4. unpow2 20.3%

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

      5. unpow2 20.3%

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

      6. hypot-define 49.3%

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

   4. Applied egg-rr 49.3%

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

   5. Taylor expanded in C around inf 66.9%

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

   6. Taylor expanded in A around inf 66.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.2e-60)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.2e-264)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 2e-32)
       (* 180.0 (/ (atan (/ (- A) B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.2e-60) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.2e-264) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 2e-32) {
		tmp = 180.0 * (atan((-A / 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 <= -2.2e-60) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.2e-264) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 2e-32) {
		tmp = 180.0 * (Math.atan((-A / 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 <= -2.2e-60:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.2e-264:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 2e-32:
		tmp = 180.0 * (math.atan((-A / 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 <= -2.2e-60)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.2e-264)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 2e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / 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 <= -2.2e-60)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.2e-264)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 2e-32)
		tmp = 180.0 * (atan((-A / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.2e-60], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-264], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e-32], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $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 < -2.1999999999999999e-60

   1. Initial program 40.9%

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

   3. Taylor expanded in B around -inf 57.7%

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

   if -2.1999999999999999e-60 < B < 2.19999999999999994e-264

   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. Taylor expanded in B around inf 49.2%

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

   4. Taylor expanded in C around inf 39.9%

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

   if 2.19999999999999994e-264 < B < 2.00000000000000011e-32

   1. Initial program 52.3%

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

   3. Taylor expanded in B around inf 46.2%

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

   4. Taylor expanded in A around inf 35.5%

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

      1. associate-*r/ 35.5%

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

      2. mul-1-neg 35.5%

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

   6. Simplified 35.5%

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

   if 2.00000000000000011e-32 < B

   1. Initial program 51.5%

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

   3. Taylor expanded in B around inf 65.6%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-88}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-101)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8e-88) (/ (* 180.0 (atan 0.0)) PI) (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-101) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8e-88) {
		tmp = (180.0 * atan(0.0)) / ((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 <= -7.2e-101) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8e-88) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.2e-101:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8e-88:
		tmp = (180.0 * math.atan(0.0)) / 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 <= -7.2e-101)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8e-88)
		tmp = Float64(Float64(180.0 * atan(0.0)) / 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 <= -7.2e-101)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8e-88)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.2e-101], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8e-88], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.19999999999999999e-101

   1. Initial program 45.8%

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

   3. Taylor expanded in B around -inf 53.6%

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

   if -7.19999999999999999e-101 < B < 7.99999999999999947e-88

   1. Initial program 52.6%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 52.6%

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

      3. *-un-lft-identity 52.6%

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

      4. unpow2 52.6%

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

      5. unpow2 52.6%

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

      6. hypot-define 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. Step-by-step derivation

      1. div-sub 49.0%

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

   6. Applied egg-rr 49.0%

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

   7. Taylor expanded in C around inf 8.7%

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

      1. distribute-lft1-in 8.7%

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

      2. metadata-eval 8.7%

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

      3. mul0-lft 31.8%

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

      4. metadata-eval 31.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   9. Simplified 31.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   if 7.99999999999999947e-88 < B

   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 57.1%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-88}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 40.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.3e-308)
   (* 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 <= -2.3e-308) {
		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 <= -2.3e-308) {
		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 <= -2.3e-308:
		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 <= -2.3e-308)
		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 <= -2.3e-308)
		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, -2.3e-308], 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 < -2.2999999999999999e-308

   1. Initial program 48.2%

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

   3. Taylor expanded in B around -inf 41.4%

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

   if -2.2999999999999999e-308 < B

   1. Initial program 52.3%

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

   3. Taylor expanded in B around inf 40.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.4% 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 50.2%

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

3. Taylor expanded in B around inf 20.4%

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

4. Final simplification 20.4%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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)))