ABCF->ab-angle angle

Percentage Accurate: 54.8% → 80.7%

Time: 24.7s

Alternatives: 14

Speedup: 1.9×

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: 54.8% 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: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.5e+24)
   (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
   (* (atan (/ (- (- C A) (hypot B (- A C))) B)) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.5e+24) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.5e+24) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.5e+24:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = math.atan((((C - A) - math.hypot(B, (A - C))) / B)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.5e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.5e+24)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.5e+24], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.4999999999999996e24

   1. Initial program 12.7%

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

   3. Taylor expanded in A around -inf 78.6%

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

      1. associate-*r/ 78.7%

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

      2. associate-*r/ 78.7%

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

   5. Applied egg-rr 78.7%

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

   if -6.4999999999999996e24 < A

   1. Initial program 65.3%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in C around 0 65.3%

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

   7. Simplified 86.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+23}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4e+23)
   (/ (* 180.0 (atan (/ (* 0.5 B) A))) 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 <= -4e+23) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((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 <= -4e+23) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / 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 <= -4e+23:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / 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 <= -4e+23)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / 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 <= -4e+23)
		tmp = (180.0 * atan(((0.5 * B) / A))) / 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, -4e+23], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.9999999999999997e23

   1. Initial program 12.7%

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

   3. Taylor expanded in A around -inf 78.6%

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

      1. associate-*r/ 78.7%

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

      2. associate-*r/ 78.7%

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

   5. Applied egg-rr 78.7%

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

   if -3.9999999999999997e23 < A

   1. Initial program 65.3%

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

   3. Simplified 86.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+23}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.5e+24)
   (/ (* 180.0 (atan (/ (* 0.5 B) A))) 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 <= -6.5e+24) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((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 <= -6.5e+24) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / 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 <= -6.5e+24:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / 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 <= -6.5e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / 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 <= -6.5e+24)
		tmp = (180.0 * atan(((0.5 * B) / A))) / 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, -6.5e+24], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -6.4999999999999996e24

   1. Initial program 12.7%

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

   3. Taylor expanded in A around -inf 78.6%

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

      1. associate-*r/ 78.7%

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

      2. associate-*r/ 78.7%

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

   5. Applied egg-rr 78.7%

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

   if -6.4999999999999996e24 < A

   1. Initial program 65.3%

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

   3. Simplified 86.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5e+16)
   (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
   (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e+16) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e+16) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5e+16:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5e+16)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5e+16)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5e+16], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5e16

   1. Initial program 12.7%

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

   3. Taylor expanded in A around -inf 78.6%

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

      1. associate-*r/ 78.7%

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

      2. associate-*r/ 78.7%

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

   5. Applied egg-rr 78.7%

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

   if -5e16 < A

   1. Initial program 65.3%

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

   3. Taylor expanded in C around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-neg-frac2 54.3%

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

      3. +-commutative 54.3%

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

      4. unpow2 54.3%

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

      5. unpow2 54.3%

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

      6. hypot-define 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.3 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-303}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* -180.0 (atan (/ A B))) PI))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= B -5.3e-27)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4.8e-166)
       (* 180.0 (/ (atan (/ C B)) PI))
       (if (<= B -7.5e-215)
         t_1
         (if (<= B 1.12e-303)
           t_0
           (if (<= B 2.5e-254)
             (* 180.0 (/ (atan 0.0) PI))
             (if (<= B 9.6e-118)
               t_0
               (if (<= B 1.2e-36) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (-180.0 * atan((A / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (B <= -5.3e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4.8e-166) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= -7.5e-215) {
		tmp = t_1;
	} else if (B <= 1.12e-303) {
		tmp = t_0;
	} else if (B <= 2.5e-254) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 9.6e-118) {
		tmp = t_0;
	} else if (B <= 1.2e-36) {
		tmp = t_1;
	} 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((A / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (B <= -5.3e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4.8e-166) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= -7.5e-215) {
		tmp = t_1;
	} else if (B <= 1.12e-303) {
		tmp = t_0;
	} else if (B <= 2.5e-254) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 9.6e-118) {
		tmp = t_0;
	} else if (B <= 1.2e-36) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-180.0 * math.atan((A / B))) / math.pi
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if B <= -5.3e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4.8e-166:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= -7.5e-215:
		tmp = t_1
	elif B <= 1.12e-303:
		tmp = t_0
	elif B <= 2.5e-254:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 9.6e-118:
		tmp = t_0
	elif B <= 1.2e-36:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (B <= -5.3e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4.8e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= -7.5e-215)
		tmp = t_1;
	elseif (B <= 1.12e-303)
		tmp = t_0;
	elseif (B <= 2.5e-254)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 9.6e-118)
		tmp = t_0;
	elseif (B <= 1.2e-36)
		tmp = t_1;
	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((A / B))) / pi;
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (B <= -5.3e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4.8e-166)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= -7.5e-215)
		tmp = t_1;
	elseif (B <= 1.12e-303)
		tmp = t_0;
	elseif (B <= 2.5e-254)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 9.6e-118)
		tmp = t_0;
	elseif (B <= 1.2e-36)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.3e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.8e-166], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.5e-215], t$95$1, If[LessEqual[B, 1.12e-303], t$95$0, If[LessEqual[B, 2.5e-254], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.6e-118], t$95$0, If[LessEqual[B, 1.2e-36], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -5.30000000000000006e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -5.30000000000000006e-27 < B < -4.7999999999999997e-166

   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. Step-by-step derivation

      1. +-commutative 71.8%

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

      2. unpow2 71.8%

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

      3. unpow2 71.8%

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

      4. hypot-undefine 72.1%

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

      5. add-cube-cbrt 71.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 71.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in C around inf 49.8%

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

   if -4.7999999999999997e-166 < B < -7.49999999999999986e-215 or 9.6000000000000006e-118 < B < 1.2e-36

   1. Initial program 43.1%

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

   3. Taylor expanded in A around -inf 61.9%

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

   if -7.49999999999999986e-215 < B < 1.1199999999999999e-303 or 2.5000000000000002e-254 < B < 9.6000000000000006e-118

   1. Initial program 68.4%

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

      1. +-commutative 68.4%

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

      2. unpow2 68.4%

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

      3. unpow2 68.4%

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

      4. hypot-undefine 82.1%

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

      5. add-cube-cbrt 70.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 68.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 65.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 65.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 65.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 65.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 65.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 65.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 68.0%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 68.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 54.8%

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

      1. associate-*r/ 54.8%

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

      2. mul-1-neg 54.8%

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

   7. Simplified 54.8%

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

      1. associate-*r/ 54.8%

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

      2. distribute-frac-neg 54.8%

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

      3. atan-neg 54.8%

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

   9. Applied egg-rr 54.8%

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

       1. distribute-rgt-neg-out 54.8%

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

       2. distribute-lft-neg-in 54.8%

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

       3. metadata-eval 54.8%

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

   11. Simplified 54.8%

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

   if 1.1199999999999999e-303 < B < 2.5000000000000002e-254

   1. Initial program 27.7%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in C around inf 38.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in B around 0 76.1%

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

      1. distribute-rgt1-in 76.1%

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

      2. metadata-eval 76.1%

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

      3. mul0-lft 76.1%

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

      4. div0 76.1%

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

      5. metadata-eval 76.1%

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

   8. Simplified 76.1%

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

   if 1.2e-36 < B

   1. Initial program 53.7%

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

   3. Taylor expanded in B around inf 65.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.3 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-303}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-118}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.25 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-116}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* -180.0 (atan (/ A B))) PI))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= B -1.25e-27)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4e-166)
       (* 180.0 (/ (atan (/ C B)) PI))
       (if (<= B -1.42e-216)
         t_1
         (if (<= B -2.5e-266)
           t_0
           (if (<= B 4.3e-240)
             (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
             (if (<= B 7.4e-116)
               t_0
               (if (<= B 1.25e-37) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (-180.0 * atan((A / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (B <= -1.25e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4e-166) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= -1.42e-216) {
		tmp = t_1;
	} else if (B <= -2.5e-266) {
		tmp = t_0;
	} else if (B <= 4.3e-240) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 7.4e-116) {
		tmp = t_0;
	} else if (B <= 1.25e-37) {
		tmp = t_1;
	} 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((A / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (B <= -1.25e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4e-166) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= -1.42e-216) {
		tmp = t_1;
	} else if (B <= -2.5e-266) {
		tmp = t_0;
	} else if (B <= 4.3e-240) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 7.4e-116) {
		tmp = t_0;
	} else if (B <= 1.25e-37) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-180.0 * math.atan((A / B))) / math.pi
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if B <= -1.25e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4e-166:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= -1.42e-216:
		tmp = t_1
	elif B <= -2.5e-266:
		tmp = t_0
	elif B <= 4.3e-240:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 7.4e-116:
		tmp = t_0
	elif B <= 1.25e-37:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (B <= -1.25e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= -1.42e-216)
		tmp = t_1;
	elseif (B <= -2.5e-266)
		tmp = t_0;
	elseif (B <= 4.3e-240)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 7.4e-116)
		tmp = t_0;
	elseif (B <= 1.25e-37)
		tmp = t_1;
	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((A / B))) / pi;
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (B <= -1.25e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4e-166)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= -1.42e-216)
		tmp = t_1;
	elseif (B <= -2.5e-266)
		tmp = t_0;
	elseif (B <= 4.3e-240)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 7.4e-116)
		tmp = t_0;
	elseif (B <= 1.25e-37)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.25e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4e-166], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.42e-216], t$95$1, If[LessEqual[B, -2.5e-266], t$95$0, If[LessEqual[B, 4.3e-240], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.4e-116], t$95$0, If[LessEqual[B, 1.25e-37], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.25e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -1.25e-27 < B < -4.00000000000000016e-166

   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. Step-by-step derivation

      1. +-commutative 71.8%

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

      2. unpow2 71.8%

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

      3. unpow2 71.8%

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

      4. hypot-undefine 72.1%

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

      5. add-cube-cbrt 71.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 71.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 71.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 71.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in C around inf 49.8%

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

   if -4.00000000000000016e-166 < B < -1.42000000000000004e-216 or 7.4000000000000005e-116 < B < 1.2499999999999999e-37

   1. Initial program 43.1%

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

   3. Taylor expanded in A around -inf 61.9%

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

   if -1.42000000000000004e-216 < B < -2.49999999999999996e-266 or 4.30000000000000013e-240 < B < 7.4000000000000005e-116

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. unpow2 70.0%

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

      3. unpow2 70.0%

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

      4. hypot-undefine 84.7%

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

      5. add-cube-cbrt 75.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 72.5%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 72.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 58.5%

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

      1. associate-*r/ 58.5%

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

      2. mul-1-neg 58.5%

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

   7. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

      2. distribute-frac-neg 58.5%

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

      3. atan-neg 58.5%

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

   9. Applied egg-rr 58.5%

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

       1. distribute-rgt-neg-out 58.5%

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

       2. distribute-lft-neg-in 58.5%

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

       3. metadata-eval 58.5%

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

   11. Simplified 58.5%

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

   if -2.49999999999999996e-266 < B < 4.30000000000000013e-240

   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. Step-by-step derivation

   3. Simplified 63.5%

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

   5. Taylor expanded in C around inf 35.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in A around 0 57.2%

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

      1. associate-*r/ 57.2%

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

   8. Simplified 57.2%

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

   if 1.2499999999999999e-37 < B

   1. Initial program 53.7%

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

   3. Taylor expanded in B around inf 65.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-116}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.5 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* -180.0 (atan (/ A B))) PI))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= B -3.5e-26)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2e-166)
       (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
       (if (<= B -7.8e-215)
         t_1
         (if (<= B -2.3e-266)
           t_0
           (if (<= B 6.6e-253)
             (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
             (if (<= B 2.1e-119)
               t_0
               (if (<= B 5.5e-36) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (-180.0 * atan((A / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (B <= -3.5e-26) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2e-166) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= -7.8e-215) {
		tmp = t_1;
	} else if (B <= -2.3e-266) {
		tmp = t_0;
	} else if (B <= 6.6e-253) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 2.1e-119) {
		tmp = t_0;
	} else if (B <= 5.5e-36) {
		tmp = t_1;
	} 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((A / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (B <= -3.5e-26) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2e-166) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= -7.8e-215) {
		tmp = t_1;
	} else if (B <= -2.3e-266) {
		tmp = t_0;
	} else if (B <= 6.6e-253) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 2.1e-119) {
		tmp = t_0;
	} else if (B <= 5.5e-36) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-180.0 * math.atan((A / B))) / math.pi
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if B <= -3.5e-26:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2e-166:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= -7.8e-215:
		tmp = t_1
	elif B <= -2.3e-266:
		tmp = t_0
	elif B <= 6.6e-253:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 2.1e-119:
		tmp = t_0
	elif B <= 5.5e-36:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (B <= -3.5e-26)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= -7.8e-215)
		tmp = t_1;
	elseif (B <= -2.3e-266)
		tmp = t_0;
	elseif (B <= 6.6e-253)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 2.1e-119)
		tmp = t_0;
	elseif (B <= 5.5e-36)
		tmp = t_1;
	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((A / B))) / pi;
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (B <= -3.5e-26)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2e-166)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= -7.8e-215)
		tmp = t_1;
	elseif (B <= -2.3e-266)
		tmp = t_0;
	elseif (B <= 6.6e-253)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 2.1e-119)
		tmp = t_0;
	elseif (B <= 5.5e-36)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.5e-26], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-166], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.8e-215], t$95$1, If[LessEqual[B, -2.3e-266], t$95$0, If[LessEqual[B, 6.6e-253], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-119], t$95$0, If[LessEqual[B, 5.5e-36], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -3.49999999999999985e-26

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -3.49999999999999985e-26 < B < -2.00000000000000008e-166

   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. Step-by-step derivation

   3. Simplified 71.8%

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

   5. Taylor expanded in C around -inf 49.8%

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

   if -2.00000000000000008e-166 < B < -7.7999999999999999e-215 or 2.1e-119 < B < 5.49999999999999984e-36

   1. Initial program 43.1%

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

   3. Taylor expanded in A around -inf 61.9%

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

   if -7.7999999999999999e-215 < B < -2.29999999999999996e-266 or 6.6000000000000002e-253 < B < 2.1e-119

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. unpow2 70.0%

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

      3. unpow2 70.0%

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

      4. hypot-undefine 84.7%

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

      5. add-cube-cbrt 75.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 69.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 69.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 72.5%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 72.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 58.5%

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

      1. associate-*r/ 58.5%

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

      2. mul-1-neg 58.5%

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

   7. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

      2. distribute-frac-neg 58.5%

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

      3. atan-neg 58.5%

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

   9. Applied egg-rr 58.5%

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

       1. distribute-rgt-neg-out 58.5%

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

       2. distribute-lft-neg-in 58.5%

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

       3. metadata-eval 58.5%

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

   11. Simplified 58.5%

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

   if -2.29999999999999996e-266 < B < 6.6000000000000002e-253

   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. Step-by-step derivation

   3. Simplified 63.5%

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

   5. Taylor expanded in C around inf 35.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in A around 0 57.2%

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

      1. associate-*r/ 57.2%

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

   8. Simplified 57.2%

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

   if 5.49999999999999984e-36 < B

   1. Initial program 53.7%

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

   3. Taylor expanded in B around inf 65.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.5 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.45 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= B -2.45e-27)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4.4e-166)
       (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
       (if (<= B -3.2e-216)
         t_0
         (if (<= B -3.7e-266)
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
           (if (<= B 5.5e-250)
             (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
             (if (<= B 3.3e-115)
               (/ (* -180.0 (atan (/ A B))) PI)
               (if (<= B 2.65e-36) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (B <= -2.45e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4.4e-166) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= -3.2e-216) {
		tmp = t_0;
	} else if (B <= -3.7e-266) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 5.5e-250) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 3.3e-115) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else if (B <= 2.65e-36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (B <= -2.45e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4.4e-166) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= -3.2e-216) {
		tmp = t_0;
	} else if (B <= -3.7e-266) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 5.5e-250) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 3.3e-115) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else if (B <= 2.65e-36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if B <= -2.45e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4.4e-166:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= -3.2e-216:
		tmp = t_0
	elif B <= -3.7e-266:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 5.5e-250:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 3.3e-115:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	elif B <= 2.65e-36:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (B <= -2.45e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4.4e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= -3.2e-216)
		tmp = t_0;
	elseif (B <= -3.7e-266)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 5.5e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 3.3e-115)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	elseif (B <= 2.65e-36)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (B <= -2.45e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4.4e-166)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= -3.2e-216)
		tmp = t_0;
	elseif (B <= -3.7e-266)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 5.5e-250)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 3.3e-115)
		tmp = (-180.0 * atan((A / B))) / pi;
	elseif (B <= 2.65e-36)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.45e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.4e-166], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.2e-216], t$95$0, If[LessEqual[B, -3.7e-266], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.5e-250], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.3e-115], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.65e-36], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -2.44999999999999988e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -2.44999999999999988e-27 < B < -4.4000000000000002e-166

   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. Step-by-step derivation

   3. Simplified 71.8%

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

   5. Taylor expanded in C around -inf 49.8%

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

   if -4.4000000000000002e-166 < B < -3.20000000000000026e-216 or 3.2999999999999999e-115 < B < 2.6499999999999999e-36

   1. Initial program 43.1%

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

   3. Taylor expanded in A around -inf 61.9%

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

   if -3.20000000000000026e-216 < B < -3.7000000000000003e-266

   1. Initial program 78.8%

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

   3. Taylor expanded in A around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -3.7000000000000003e-266 < B < 5.5e-250

   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. Step-by-step derivation

   3. Simplified 63.5%

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

   5. Taylor expanded in C around inf 35.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in A around 0 57.2%

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

      1. associate-*r/ 57.2%

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

   8. Simplified 57.2%

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

   if 5.5e-250 < B < 3.2999999999999999e-115

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. unpow2 66.9%

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

      3. unpow2 66.9%

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

      4. hypot-undefine 83.1%

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

      5. add-cube-cbrt 74.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 70.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 70.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 70.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-frac-neg 55.2%

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

      3. atan-neg 55.2%

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

   9. Applied egg-rr 55.2%

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

       1. distribute-rgt-neg-out 55.2%

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

       2. distribute-lft-neg-in 55.2%

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

       3. metadata-eval 55.2%

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

   11. Simplified 55.2%

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

   if 2.6499999999999999e-36 < B

   1. Initial program 53.7%

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

   3. Taylor expanded in B around inf 65.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.45 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.55 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-117}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.25e-27)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -2.55e-166)
     (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
     (if (<= B -8.8e-215)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (if (<= B -3.7e-266)
         (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
         (if (<= B 3.5e-246)
           (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
           (if (<= B 1.05e-117)
             (/ (* -180.0 (atan (/ A B))) PI)
             (if (<= B 7.5e-35)
               (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.25e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.55e-166) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= -8.8e-215) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -3.7e-266) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 3.5e-246) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 1.05e-117) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else if (B <= 7.5e-35) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.25e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.55e-166) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= -8.8e-215) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -3.7e-266) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 3.5e-246) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 1.05e-117) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else if (B <= 7.5e-35) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.25e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.55e-166:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= -8.8e-215:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -3.7e-266:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 3.5e-246:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 1.05e-117:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	elif B <= 7.5e-35:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.25e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.55e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= -8.8e-215)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -3.7e-266)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 3.5e-246)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 1.05e-117)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	elseif (B <= 7.5e-35)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.25e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.55e-166)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= -8.8e-215)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -3.7e-266)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 3.5e-246)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 1.05e-117)
		tmp = (-180.0 * atan((A / B))) / pi;
	elseif (B <= 7.5e-35)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.25e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.55e-166], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.8e-215], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.7e-266], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e-246], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.05e-117], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.5e-35], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -1.25e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -1.25e-27 < B < -2.5500000000000001e-166

   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. Step-by-step derivation

   3. Simplified 71.8%

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

   5. Taylor expanded in C around -inf 49.8%

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

   if -2.5500000000000001e-166 < B < -8.79999999999999985e-215

   1. Initial program 36.4%

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

   3. Taylor expanded in A around -inf 68.1%

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

   if -8.79999999999999985e-215 < B < -3.7000000000000003e-266

   1. Initial program 78.8%

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

   3. Taylor expanded in A around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -3.7000000000000003e-266 < B < 3.5000000000000002e-246

   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. Step-by-step derivation

   3. Simplified 63.5%

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

   5. Taylor expanded in C around inf 35.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in A around 0 57.2%

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

      1. associate-*r/ 57.2%

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

   8. Simplified 57.2%

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

   if 3.5000000000000002e-246 < B < 1.05e-117

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. unpow2 66.9%

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

      3. unpow2 66.9%

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

      4. hypot-undefine 83.1%

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

      5. add-cube-cbrt 74.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 70.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 66.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 70.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 70.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-frac-neg 55.2%

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

      3. atan-neg 55.2%

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

   9. Applied egg-rr 55.2%

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

       1. distribute-rgt-neg-out 55.2%

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

       2. distribute-lft-neg-in 55.2%

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

       3. metadata-eval 55.2%

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

   11. Simplified 55.2%

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

   if 1.05e-117 < B < 7.5e-35

   1. Initial program 47.1%

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

   3. Taylor expanded in A around -inf 58.3%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r/ 58.4%

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

   5. Applied egg-rr 58.4%

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

   if 7.5e-35 < B

   1. Initial program 53.7%

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

   3. Taylor expanded in B around inf 65.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.55 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-117}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-246}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-86}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -1.95e-27)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -7.5e-246)
       t_0
       (if (<= B 6e-257)
         (* 180.0 (/ (atan 0.0) PI))
         (if (<= B 1.55e-86) 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 <= -1.95e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.5e-246) {
		tmp = t_0;
	} else if (B <= 6e-257) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 1.55e-86) {
		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 <= -1.95e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.5e-246) {
		tmp = t_0;
	} else if (B <= 6e-257) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 1.55e-86) {
		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 <= -1.95e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.5e-246:
		tmp = t_0
	elif B <= 6e-257:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 1.55e-86:
		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 <= -1.95e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.5e-246)
		tmp = t_0;
	elseif (B <= 6e-257)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 1.55e-86)
		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 <= -1.95e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.5e-246)
		tmp = t_0;
	elseif (B <= 6e-257)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 1.55e-86)
		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, -1.95e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.5e-246], t$95$0, If[LessEqual[B, 6e-257], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.55e-86], 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 < -1.94999999999999986e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -1.94999999999999986e-27 < B < -7.50000000000000049e-246 or 5.9999999999999999e-257 < B < 1.54999999999999994e-86

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. unpow2 65.8%

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

      3. unpow2 65.8%

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

      4. hypot-undefine 77.5%

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

      5. add-cube-cbrt 70.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 69.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 65.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 65.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 65.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 65.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 65.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 65.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 69.0%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 69.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in C around inf 46.8%

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

   if -7.50000000000000049e-246 < B < 5.9999999999999999e-257

   1. Initial program 47.7%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in C around inf 32.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in B around 0 52.6%

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

      1. distribute-rgt1-in 52.6%

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

      2. metadata-eval 52.6%

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

      3. mul0-lft 52.6%

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

      4. div0 52.6%

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

      5. metadata-eval 52.6%

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

   8. Simplified 52.6%

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

   if 1.54999999999999994e-86 < B

   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 inf 59.4%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-95}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.5e-27)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -8.2e-246)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 3e-250)
       (* 180.0 (/ (atan 0.0) PI))
       (if (<= B 5e-95)
         (/ (* -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 <= -5.5e-27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.2e-246) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 3e-250) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 5e-95) {
		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 <= -5.5e-27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.2e-246) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 3e-250) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 5e-95) {
		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 <= -5.5e-27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.2e-246:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 3e-250:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 5e-95:
		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 <= -5.5e-27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.2e-246)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 3e-250)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 5e-95)
		tmp = Float64(Float64(-180.0 * atan(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 <= -5.5e-27)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.2e-246)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 3e-250)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 5e-95)
		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, -5.5e-27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.2e-246], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3e-250], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-95], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -5.5000000000000002e-27

   1. Initial program 40.7%

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

   3. Taylor expanded in B around -inf 61.0%

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

   if -5.5000000000000002e-27 < B < -8.19999999999999971e-246

   1. Initial program 64.8%

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

      1. +-commutative 64.8%

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

      2. unpow2 64.8%

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

      3. unpow2 64.8%

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

      4. hypot-undefine 75.5%

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

      5. add-cube-cbrt 68.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 68.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 64.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 64.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 64.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 68.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 68.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in C around inf 47.3%

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

   if -8.19999999999999971e-246 < B < 3.00000000000000016e-250

   1. Initial program 47.7%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in C around inf 32.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in B around 0 52.6%

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

      1. distribute-rgt1-in 52.6%

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

      2. metadata-eval 52.6%

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

      3. mul0-lft 52.6%

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

      4. div0 52.6%

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

      5. metadata-eval 52.6%

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

   8. Simplified 52.6%

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

   if 3.00000000000000016e-250 < B < 4.9999999999999998e-95

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. unpow2 70.4%

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

      3. unpow2 70.4%

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

      4. hypot-undefine 84.8%

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

      5. add-cube-cbrt 76.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)} \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right) \cdot \sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}}\right)\right)}{\pi} \]

      6. pow3 73.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(B, A - C\right)}\right)}^{3}}\right)\right)}{\pi} \]

      7. hypot-undefine 70.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}\right)}^{3}\right)\right)}{\pi} \]

      8. unpow2 70.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}\right)}^{3}\right)\right)}{\pi} \]

      9. unpow2 70.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      10. +-commutative 70.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}\right)}^{3}\right)\right)}{\pi} \]

      11. unpow2 70.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}\right)}^{3}\right)\right)}{\pi} \]

      12. unpow2 70.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}\right)}^{3}\right)\right)}{\pi} \]

      13. hypot-define 73.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{hypot}\left(A - C, B\right)}}\right)}^{3}\right)\right)}{\pi} \]

   4. Applied egg-rr 73.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{hypot}\left(A - C, B\right)}\right)}^{3}}\right)\right)}{\pi} \]

   5. Taylor expanded in A around inf 53.0%

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

      1. associate-*r/ 53.0%

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

      2. mul-1-neg 53.0%

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

   7. Simplified 53.0%

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

      1. associate-*r/ 53.0%

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

      2. distribute-frac-neg 53.0%

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

      3. atan-neg 53.0%

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

   9. Applied egg-rr 53.0%

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

       1. distribute-rgt-neg-out 53.0%

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

       2. distribute-lft-neg-in 53.0%

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

       3. metadata-eval 53.0%

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

   11. Simplified 53.0%

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

   if 4.9999999999999998e-95 < B

   1. Initial program 50.9%

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

   3. Taylor expanded in B around inf 57.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-95}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3e-166)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.6e-79)
     (* 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 <= -3e-166) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.6e-79) {
		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 <= -3e-166) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.6e-79) {
		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 <= -3e-166:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.6e-79:
		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 <= -3e-166)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.6e-79)
		tmp = Float64(180.0 * Float64(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 <= -3e-166)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.6e-79)
		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, -3e-166], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.6e-79], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.0000000000000003e-166

   1. Initial program 49.8%

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

   3. Taylor expanded in B around -inf 48.3%

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

   if -3.0000000000000003e-166 < B < 9.60000000000000023e-79

   1. Initial program 56.2%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in C around inf 16.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in B around 0 30.5%

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

      1. distribute-rgt1-in 30.5%

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

      2. metadata-eval 30.5%

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

      3. mul0-lft 30.5%

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

      4. div0 30.5%

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

      5. metadata-eval 30.5%

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

   8. Simplified 30.5%

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

   if 9.60000000000000023e-79 < B

   1. Initial program 52.9%

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

   3. Taylor expanded in B around inf 61.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.95e-78) (* 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 <= 1.95e-78) {
		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 <= 1.95e-78) {
		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 <= 1.95e-78:
		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 <= 1.95e-78)
		tmp = Float64(180.0 * Float64(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 <= 1.95e-78)
		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, 1.95e-78], N[(180.0 * N[(N[ArcTan[0.0], $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 < 1.9500000000000001e-78

   1. Initial program 52.7%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in C around inf 15.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right) + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}}}{B}\right)}{\pi} \]

   6. Taylor expanded in B around 0 16.2%

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

      1. distribute-rgt1-in 16.2%

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

      2. metadata-eval 16.2%

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

      3. mul0-lft 16.2%

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

      4. div0 16.2%

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

      5. metadata-eval 16.2%

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

   8. Simplified 16.2%

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

   if 1.9500000000000001e-78 < B

   1. Initial program 52.9%

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

   3. Taylor expanded in B around inf 61.3%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.8%

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

3. Taylor expanded in B around inf 24.4%

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

4. Final simplification 24.4%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024052 
(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)))