ABCF->ab-angle angle

Percentage Accurate: 53.6% → 80.9%

Time: 17.6s

Alternatives: 14

Speedup: 2.4×

Specification

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Initial Program: 53.6% 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: 80.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.05 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.05e+62)
   (* 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 <= -3.05e+62) {
		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 <= -3.05e+62) {
		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 <= -3.05e+62:
		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 <= -3.05e+62)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(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 <= -3.05e+62)
		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, -3.05e+62], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.0499999999999998e62

   1. Initial program 16.2%

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

      1. associate-*l/ 16.2%

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

      2. *-lft-identity 16.2%

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

      3. +-commutative 16.2%

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

      4. unpow2 16.2%

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

      5. unpow2 16.2%

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

      6. hypot-def 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in A around -inf 86.5%

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

   if -3.0499999999999998e62 < A

   1. Initial program 59.2%

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

      1. associate-*l/ 59.2%

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

      2. *-lft-identity 59.2%

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

      3. +-commutative 59.2%

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

      4. unpow2 59.2%

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

      5. unpow2 59.2%

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

      6. hypot-def 80.9%

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

   3. Simplified 80.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.05 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 77.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e+62)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.25e-34)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+62) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.25e-34) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+62) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.25e-34) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+62:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.25e-34:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+62)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.25e-34)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e+62)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.25e-34)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+62], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-34], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.10000000000000014e62

   1. Initial program 16.2%

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

      1. associate-*l/ 16.2%

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

      2. *-lft-identity 16.2%

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

      3. +-commutative 16.2%

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

      4. unpow2 16.2%

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

      5. unpow2 16.2%

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

      6. hypot-def 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in A around -inf 86.5%

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

   if -3.10000000000000014e62 < A < 1.2500000000000001e-34

   1. Initial program 51.5%

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

      1. associate-*l/ 51.5%

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

      2. *-lft-identity 51.5%

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

      3. +-commutative 51.5%

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

      4. unpow2 51.5%

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

      5. unpow2 51.5%

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

      6. hypot-def 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in A around 0 48.7%

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

      1. unpow2 48.7%

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

      2. unpow2 48.7%

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

      3. hypot-def 72.2%

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

   6. Simplified 72.2%

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

   if 1.2500000000000001e-34 < A

   1. Initial program 76.3%

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

      1. associate-*l/ 76.3%

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

      2. *-lft-identity 76.3%

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

      3. +-commutative 76.3%

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

      4. unpow2 76.3%

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

      5. unpow2 76.3%

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

      6. hypot-def 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in C around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. +-commutative 76.3%

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

      3. unpow2 76.3%

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

      4. unpow2 76.3%

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

      5. hypot-def 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 75.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3e+62)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 4.1e+22)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (- B A) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+62) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 4.1e+22) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+62) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 4.1e+22) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3e+62:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 4.1e+22:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3e+62)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 4.1e+22)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3e+62)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 4.1e+22)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((B - A) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3e+62], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.1e+22], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3e62

   1. Initial program 16.2%

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

      1. associate-*l/ 16.2%

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

      2. *-lft-identity 16.2%

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

      3. +-commutative 16.2%

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

      4. unpow2 16.2%

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

      5. unpow2 16.2%

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

      6. hypot-def 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in A around -inf 86.5%

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

   if -3e62 < A < 4.09999999999999979e22

   1. Initial program 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-lft-identity 53.0%

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

      3. +-commutative 53.0%

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

      4. unpow2 53.0%

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

      5. unpow2 53.0%

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

      6. hypot-def 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in A around 0 49.1%

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

      1. unpow2 49.1%

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

      2. unpow2 49.1%

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

      3. hypot-def 72.5%

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

   6. Simplified 72.5%

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

   if 4.09999999999999979e22 < A

   1. Initial program 75.9%

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

      1. associate-*r/ 75.9%

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

      2. associate-*l/ 75.9%

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

      3. associate-*l/ 75.9%

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

      4. *-lft-identity 75.9%

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

      5. sub-neg 75.9%

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

      6. associate-+l- 75.9%

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

      7. sub-neg 75.9%

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

      8. remove-double-neg 75.9%

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

      9. +-commutative 75.9%

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

      10. unpow2 75.9%

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

      11. unpow2 75.9%

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

      12. hypot-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in B around -inf 82.9%

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

      1. neg-mul-1 82.9%

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

      2. unsub-neg 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in C around 0 83.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \]

Alternative 4: 58.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -3 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1150000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B \cdot B}{B \cdot C}\right)\\ \mathbf{elif}\;A \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \left(\left(B \cdot \frac{B}{A}\right) \cdot \left(\frac{C}{A} + 1\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-162}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-240}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -3e+62)
     t_1
     (if (<= A -1150000.0)
       t_0
       (if (<= A -8.8e-29)
         (* (/ 180.0 PI) (atan (* -0.5 (/ (* B B) (* B C)))))
         (if (<= A -1.4e-65)
           (*
            180.0
            (/ (atan (/ (* 0.5 (* (* B (/ B A)) (+ (/ C A) 1.0))) B)) PI))
           (if (<= A -2e-129)
             t_1
             (if (<= A -2e-162)
               (* (/ 180.0 PI) (atan (/ (+ B C) B)))
               (if (<= A -5e-240)
                 t_0
                 (if (<= A 1.55e+168)
                   (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
                   (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -3e+62) {
		tmp = t_1;
	} else if (A <= -1150000.0) {
		tmp = t_0;
	} else if (A <= -8.8e-29) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * ((B * B) / (B * C))));
	} else if (A <= -1.4e-65) {
		tmp = 180.0 * (atan(((0.5 * ((B * (B / A)) * ((C / A) + 1.0))) / B)) / ((double) M_PI));
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= -2e-162) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (A <= -5e-240) {
		tmp = t_0;
	} else if (A <= 1.55e+168) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -3e+62) {
		tmp = t_1;
	} else if (A <= -1150000.0) {
		tmp = t_0;
	} else if (A <= -8.8e-29) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * ((B * B) / (B * C))));
	} else if (A <= -1.4e-65) {
		tmp = 180.0 * (Math.atan(((0.5 * ((B * (B / A)) * ((C / A) + 1.0))) / B)) / Math.PI);
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= -2e-162) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (A <= -5e-240) {
		tmp = t_0;
	} else if (A <= 1.55e+168) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -3e+62:
		tmp = t_1
	elif A <= -1150000.0:
		tmp = t_0
	elif A <= -8.8e-29:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * ((B * B) / (B * C))))
	elif A <= -1.4e-65:
		tmp = 180.0 * (math.atan(((0.5 * ((B * (B / A)) * ((C / A) + 1.0))) / B)) / math.pi)
	elif A <= -2e-129:
		tmp = t_1
	elif A <= -2e-162:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif A <= -5e-240:
		tmp = t_0
	elif A <= 1.55e+168:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -3e+62)
		tmp = t_1;
	elseif (A <= -1150000.0)
		tmp = t_0;
	elseif (A <= -8.8e-29)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(Float64(B * B) / Float64(B * C)))));
	elseif (A <= -1.4e-65)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * Float64(Float64(B * Float64(B / A)) * Float64(Float64(C / A) + 1.0))) / B)) / pi));
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= -2e-162)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (A <= -5e-240)
		tmp = t_0;
	elseif (A <= 1.55e+168)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - B) - A) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -3e+62)
		tmp = t_1;
	elseif (A <= -1150000.0)
		tmp = t_0;
	elseif (A <= -8.8e-29)
		tmp = (180.0 / pi) * atan((-0.5 * ((B * B) / (B * C))));
	elseif (A <= -1.4e-65)
		tmp = 180.0 * (atan(((0.5 * ((B * (B / A)) * ((C / A) + 1.0))) / B)) / pi);
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= -2e-162)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (A <= -5e-240)
		tmp = t_0;
	elseif (A <= 1.55e+168)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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[A, -3e+62], t$95$1, If[LessEqual[A, -1150000.0], t$95$0, If[LessEqual[A, -8.8e-29], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(N[(B * B), $MachinePrecision] / N[(B * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.4e-65], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * N[(N[(B * N[(B / A), $MachinePrecision]), $MachinePrecision] * N[(N[(C / A), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-129], t$95$1, If[LessEqual[A, -2e-162], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -5e-240], t$95$0, If[LessEqual[A, 1.55e+168], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if A < -3e62 or -1.4e-65 < A < -1.9999999999999999e-129

   1. Initial program 22.7%

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

      1. associate-*l/ 22.7%

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

      2. *-lft-identity 22.7%

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

      3. +-commutative 22.7%

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

      4. unpow2 22.7%

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

      5. unpow2 22.7%

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

      6. hypot-def 45.7%

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

   3. Simplified 45.7%

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

   4. Taylor expanded in A around -inf 81.3%

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

   if -3e62 < A < -1.15e6 or -1.99999999999999991e-162 < A < -5.0000000000000004e-240

   1. Initial program 50.8%

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

      1. associate-*l/ 50.7%

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

      2. *-lft-identity 50.7%

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

      3. +-commutative 50.7%

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

      4. unpow2 50.7%

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

      5. unpow2 50.7%

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

      6. hypot-def 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in B around inf 70.0%

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

      1. neg-mul-1 70.0%

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

      2. unsub-neg 70.0%

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

   6. Simplified 70.0%

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

   if -1.15e6 < A < -8.79999999999999961e-29

   1. Initial program 6.6%

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

      1. associate-*l/ 6.6%

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

      2. *-lft-identity 6.6%

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

      3. +-commutative 6.6%

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

      4. unpow2 6.6%

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

      5. unpow2 6.6%

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

      6. hypot-def 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in C around inf 33.3%

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

      1. fma-def 33.3%

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

      2. associate--l+ 52.1%

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

      3. unpow2 52.1%

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

      4. fma-def 52.1%

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

      5. unpow2 52.1%

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

      6. unpow2 52.1%

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

      7. difference-of-squares 52.1%

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

      8. distribute-rgt1-in 52.1%

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

      9. metadata-eval 52.1%

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

      10. mul0-lft 52.1%

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

      11. mul-1-neg 52.1%

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

      12. *-commutative 52.1%

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

      13. associate-*r/ 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in B around 0 52.1%

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

      1. associate-*r/ 52.1%

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

      2. associate-/l* 52.3%

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

      3. associate-/r/ 52.3%

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

      4. fma-udef 52.3%

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

      5. +-rgt-identity 52.3%

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

      6. fma-udef 52.3%

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

      7. unpow2 52.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{\color{blue}{{B}^{2}} + 0}{C \cdot B}\right) \]

      8. +-rgt-identity 52.3%

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

      9. unpow2 52.3%

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

   9. Simplified 52.3%

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

   if -8.79999999999999961e-29 < A < -1.4e-65

   1. Initial program 64.4%

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

      1. associate-*l/ 64.4%

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

      2. *-lft-identity 64.4%

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

      3. +-commutative 64.4%

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

      4. unpow2 64.4%

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

      5. unpow2 64.4%

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

      6. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in A around -inf 54.4%

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

      1. distribute-lft-out 54.4%

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

      2. associate-/l* 54.4%

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

      3. unpow2 54.4%

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

      4. unpow2 54.4%

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

      5. times-frac 73.8%

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

      6. unpow2 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in C around 0 54.4%

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

      1. +-commutative 54.4%

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

      2. unpow2 54.4%

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

      3. times-frac 54.4%

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

      4. unpow2 54.4%

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

      5. associate-/l* 73.8%

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

      6. unpow2 73.8%

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

      7. associate-/l* 73.8%

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

      8. *-lft-identity 73.8%

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

      9. distribute-rgt-out 75.6%

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

      10. associate-/r/ 75.6%

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

      11. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -1.9999999999999999e-129 < A < -1.99999999999999991e-162

   1. Initial program 45.4%

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

      1. associate-*r/ 45.4%

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

      2. associate-*l/ 45.4%

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

      3. associate-*l/ 45.4%

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

      4. *-lft-identity 45.4%

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

      5. sub-neg 45.4%

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

      6. associate-+l- 45.4%

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

      7. sub-neg 45.4%

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

      8. remove-double-neg 45.4%

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

      9. +-commutative 45.4%

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

      10. unpow2 45.4%

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

      11. unpow2 45.4%

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

      12. hypot-def 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in B around -inf 51.2%

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

      1. neg-mul-1 51.2%

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

      2. unsub-neg 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in A around 0 51.2%

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

   if -5.0000000000000004e-240 < A < 1.54999999999999998e168

   1. Initial program 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.3%

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

      3. associate-*l/ 59.3%

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

      4. *-lft-identity 59.3%

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

      5. sub-neg 59.3%

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

      6. associate-+l- 59.3%

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

      7. sub-neg 59.3%

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

      8. remove-double-neg 59.3%

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

      9. +-commutative 59.3%

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

      10. unpow2 59.3%

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

      11. unpow2 59.3%

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

      12. hypot-def 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in B around -inf 59.4%

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

      1. neg-mul-1 59.4%

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

      2. unsub-neg 59.4%

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

   6. Simplified 59.4%

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

   if 1.54999999999999998e168 < A

   1. Initial program 86.9%

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

      1. associate-*l/ 86.9%

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

      2. *-lft-identity 86.9%

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

      3. +-commutative 86.9%

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

      4. unpow2 86.9%

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

      5. unpow2 86.9%

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

      6. hypot-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in B around inf 94.9%

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

      1. neg-mul-1 94.9%

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

      2. unsub-neg 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in C around 0 94.9%

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

      1. associate-*r/ 94.9%

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

      2. neg-mul-1 94.9%

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

      3. distribute-neg-in 94.9%

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

      4. sub-neg 94.9%

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

      5. div-sub 94.9%

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

      6. distribute-frac-neg 94.9%

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

      7. *-inverses 94.9%

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

      8. sub-neg 94.9%

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

      9. metadata-eval 94.9%

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

      10. +-commutative 94.9%

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

      11. unsub-neg 94.9%

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

   9. Simplified 94.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1150000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B \cdot B}{B \cdot C}\right)\\ \mathbf{elif}\;A \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \left(\left(B \cdot \frac{B}{A}\right) \cdot \left(\frac{C}{A} + 1\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-162}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 59.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 10^{+171}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -2.6e+62)
     t_1
     (if (<= A -2.4e-67)
       t_0
       (if (<= A -2e-129)
         t_1
         (if (<= A -1.85e-239)
           t_0
           (if (<= A 1e+171)
             (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -2.6e+62) {
		tmp = t_1;
	} else if (A <= -2.4e-67) {
		tmp = t_0;
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= -1.85e-239) {
		tmp = t_0;
	} else if (A <= 1e+171) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -2.6e+62) {
		tmp = t_1;
	} else if (A <= -2.4e-67) {
		tmp = t_0;
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= -1.85e-239) {
		tmp = t_0;
	} else if (A <= 1e+171) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -2.6e+62:
		tmp = t_1
	elif A <= -2.4e-67:
		tmp = t_0
	elif A <= -2e-129:
		tmp = t_1
	elif A <= -1.85e-239:
		tmp = t_0
	elif A <= 1e+171:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -2.6e+62)
		tmp = t_1;
	elseif (A <= -2.4e-67)
		tmp = t_0;
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= -1.85e-239)
		tmp = t_0;
	elseif (A <= 1e+171)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - B) - A) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -2.6e+62)
		tmp = t_1;
	elseif (A <= -2.4e-67)
		tmp = t_0;
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= -1.85e-239)
		tmp = t_0;
	elseif (A <= 1e+171)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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[A, -2.6e+62], t$95$1, If[LessEqual[A, -2.4e-67], t$95$0, If[LessEqual[A, -2e-129], t$95$1, If[LessEqual[A, -1.85e-239], t$95$0, If[LessEqual[A, 1e+171], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.59999999999999984e62 or -2.4e-67 < A < -1.9999999999999999e-129

   1. Initial program 22.7%

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

      1. associate-*l/ 22.7%

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

      2. *-lft-identity 22.7%

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

      3. +-commutative 22.7%

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

      4. unpow2 22.7%

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

      5. unpow2 22.7%

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

      6. hypot-def 45.7%

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

   3. Simplified 45.7%

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

   4. Taylor expanded in A around -inf 81.3%

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

   if -2.59999999999999984e62 < A < -2.4e-67 or -1.9999999999999999e-129 < A < -1.85000000000000008e-239

   1. Initial program 45.6%

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

      1. associate-*l/ 45.5%

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

      2. *-lft-identity 45.5%

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

      3. +-commutative 45.5%

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

      4. unpow2 45.5%

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

      5. unpow2 45.5%

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

      6. hypot-def 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in B around inf 54.3%

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

      1. neg-mul-1 54.3%

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

      2. unsub-neg 54.3%

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

   6. Simplified 54.3%

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

   if -1.85000000000000008e-239 < A < 9.99999999999999954e170

   1. Initial program 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.3%

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

      3. associate-*l/ 59.3%

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

      4. *-lft-identity 59.3%

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

      5. sub-neg 59.3%

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

      6. associate-+l- 59.3%

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

      7. sub-neg 59.3%

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

      8. remove-double-neg 59.3%

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

      9. +-commutative 59.3%

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

      10. unpow2 59.3%

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

      11. unpow2 59.3%

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

      12. hypot-def 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in B around -inf 59.4%

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

      1. neg-mul-1 59.4%

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

      2. unsub-neg 59.4%

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

   6. Simplified 59.4%

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

   if 9.99999999999999954e170 < A

   1. Initial program 86.9%

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

      1. associate-*l/ 86.9%

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

      2. *-lft-identity 86.9%

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

      3. +-commutative 86.9%

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

      4. unpow2 86.9%

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

      5. unpow2 86.9%

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

      6. hypot-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in B around inf 94.9%

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

      1. neg-mul-1 94.9%

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

      2. unsub-neg 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in C around 0 94.9%

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

      1. associate-*r/ 94.9%

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

      2. neg-mul-1 94.9%

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

      3. distribute-neg-in 94.9%

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

      4. sub-neg 94.9%

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

      5. div-sub 94.9%

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

      6. distribute-frac-neg 94.9%

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

      7. *-inverses 94.9%

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

      8. sub-neg 94.9%

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

      9. metadata-eval 94.9%

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

      10. +-commutative 94.9%

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

      11. unsub-neg 94.9%

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

   9. Simplified 94.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{+171}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 57.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.04 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.3 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (+ B C) B)))))
   (if (<= A -4.8e-31)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -1.04e-168)
       t_0
       (if (<= A -4.3e-201)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A -3.4e-234)
           (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
           (if (<= A 5.5e-68)
             t_0
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double tmp;
	if (A <= -4.8e-31) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.04e-168) {
		tmp = t_0;
	} else if (A <= -4.3e-201) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= -3.4e-234) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (A <= 5.5e-68) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double tmp;
	if (A <= -4.8e-31) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.04e-168) {
		tmp = t_0;
	} else if (A <= -4.3e-201) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= -3.4e-234) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (A <= 5.5e-68) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B + C) / B))
	tmp = 0
	if A <= -4.8e-31:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.04e-168:
		tmp = t_0
	elif A <= -4.3e-201:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= -3.4e-234:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif A <= 5.5e-68:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)))
	tmp = 0.0
	if (A <= -4.8e-31)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.04e-168)
		tmp = t_0;
	elseif (A <= -4.3e-201)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= -3.4e-234)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (A <= 5.5e-68)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B + C) / B));
	tmp = 0.0;
	if (A <= -4.8e-31)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.04e-168)
		tmp = t_0;
	elseif (A <= -4.3e-201)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= -3.4e-234)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (A <= 5.5e-68)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -4.8e-31], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.04e-168], t$95$0, If[LessEqual[A, -4.3e-201], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.4e-234], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.5e-68], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -4.8e-31

   1. Initial program 18.6%

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

      1. associate-*l/ 18.5%

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

      2. *-lft-identity 18.5%

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

      3. +-commutative 18.5%

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

      4. unpow2 18.5%

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

      5. unpow2 18.5%

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

      6. hypot-def 48.4%

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

   3. Simplified 48.4%

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

   4. Taylor expanded in A around -inf 71.0%

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

   if -4.8e-31 < A < -1.04000000000000006e-168 or -3.39999999999999986e-234 < A < 5.5000000000000003e-68

   1. Initial program 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*l/ 55.8%

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

      3. associate-*l/ 55.8%

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

      4. *-lft-identity 55.8%

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

      5. sub-neg 55.8%

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

      6. associate-+l- 55.8%

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

      7. sub-neg 55.8%

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

      8. remove-double-neg 55.8%

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

      9. +-commutative 55.8%

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

      10. unpow2 55.8%

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

      11. unpow2 55.8%

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

      12. hypot-def 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in B around -inf 52.8%

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

      1. neg-mul-1 52.8%

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

      2. unsub-neg 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in A around 0 50.3%

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

   if -1.04000000000000006e-168 < A < -4.2999999999999997e-201

   1. Initial program 53.9%

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

      1. associate-*l/ 53.9%

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

      2. *-lft-identity 53.9%

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

      3. +-commutative 53.9%

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

      4. unpow2 53.9%

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

      5. unpow2 53.9%

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

      6. hypot-def 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in B around inf 67.5%

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

   if -4.2999999999999997e-201 < A < -3.39999999999999986e-234

   1. Initial program 51.5%

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

      1. associate-*l/ 51.5%

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

      2. *-lft-identity 51.5%

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

      3. +-commutative 51.5%

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

      4. unpow2 51.5%

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

      5. unpow2 51.5%

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

      6. hypot-def 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in C around -inf 39.1%

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

   if 5.5000000000000003e-68 < A

   1. Initial program 74.4%

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

      1. associate-*l/ 74.4%

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

      2. *-lft-identity 74.4%

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

      3. +-commutative 74.4%

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

      4. unpow2 74.4%

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

      5. unpow2 74.4%

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

      6. hypot-def 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in B around inf 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in C around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

      3. distribute-neg-in 77.9%

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

      4. sub-neg 77.9%

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

      5. div-sub 77.9%

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

      6. distribute-frac-neg 77.9%

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

      7. *-inverses 77.9%

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

      8. sub-neg 77.9%

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

      9. metadata-eval 77.9%

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

      10. +-commutative 77.9%

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

      11. unsub-neg 77.9%

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

   9. Simplified 77.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.04 \cdot 10^{-168}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq -4.3 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -9 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+178}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -2.6e+62)
     t_1
     (if (<= A -9e-68)
       t_0
       (if (<= A -2e-129)
         t_1
         (if (<= A 7.8e-17)
           t_0
           (if (<= A 7.5e+178)
             (* (/ 180.0 PI) (atan (/ (- B A) B)))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -2.6e+62) {
		tmp = t_1;
	} else if (A <= -9e-68) {
		tmp = t_0;
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= 7.8e-17) {
		tmp = t_0;
	} else if (A <= 7.5e+178) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -2.6e+62) {
		tmp = t_1;
	} else if (A <= -9e-68) {
		tmp = t_0;
	} else if (A <= -2e-129) {
		tmp = t_1;
	} else if (A <= 7.8e-17) {
		tmp = t_0;
	} else if (A <= 7.5e+178) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -2.6e+62:
		tmp = t_1
	elif A <= -9e-68:
		tmp = t_0
	elif A <= -2e-129:
		tmp = t_1
	elif A <= 7.8e-17:
		tmp = t_0
	elif A <= 7.5e+178:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -2.6e+62)
		tmp = t_1;
	elseif (A <= -9e-68)
		tmp = t_0;
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= 7.8e-17)
		tmp = t_0;
	elseif (A <= 7.5e+178)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - B) - A) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -2.6e+62)
		tmp = t_1;
	elseif (A <= -9e-68)
		tmp = t_0;
	elseif (A <= -2e-129)
		tmp = t_1;
	elseif (A <= 7.8e-17)
		tmp = t_0;
	elseif (A <= 7.5e+178)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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[A, -2.6e+62], t$95$1, If[LessEqual[A, -9e-68], t$95$0, If[LessEqual[A, -2e-129], t$95$1, If[LessEqual[A, 7.8e-17], t$95$0, If[LessEqual[A, 7.5e+178], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.59999999999999984e62 or -8.99999999999999998e-68 < A < -1.9999999999999999e-129

   1. Initial program 22.7%

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

      1. associate-*l/ 22.7%

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

      2. *-lft-identity 22.7%

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

      3. +-commutative 22.7%

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

      4. unpow2 22.7%

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

      5. unpow2 22.7%

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

      6. hypot-def 45.7%

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

   3. Simplified 45.7%

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

   4. Taylor expanded in A around -inf 81.3%

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

   if -2.59999999999999984e62 < A < -8.99999999999999998e-68 or -1.9999999999999999e-129 < A < 7.79999999999999979e-17

   1. Initial program 52.2%

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

      1. associate-*l/ 52.2%

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

      2. *-lft-identity 52.2%

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

      3. +-commutative 52.2%

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

      4. unpow2 52.2%

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

      5. unpow2 52.2%

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

      6. hypot-def 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in B around inf 50.7%

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

      1. neg-mul-1 50.7%

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

      2. unsub-neg 50.7%

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

   6. Simplified 50.7%

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

   if 7.79999999999999979e-17 < A < 7.4999999999999995e178

   1. Initial program 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-*l/ 65.0%

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

      3. associate-*l/ 65.0%

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

      4. *-lft-identity 65.0%

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

      5. sub-neg 65.0%

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

      6. associate-+l- 65.0%

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

      7. sub-neg 65.0%

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

      8. remove-double-neg 65.0%

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

      9. +-commutative 65.0%

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

      10. unpow2 65.0%

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

      11. unpow2 65.0%

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

      12. hypot-def 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in B around -inf 76.9%

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

      1. neg-mul-1 76.9%

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

      2. unsub-neg 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in C around 0 77.3%

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

   if 7.4999999999999995e178 < A

   1. Initial program 89.3%

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

      1. associate-*l/ 89.3%

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

      2. *-lft-identity 89.3%

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

      3. +-commutative 89.3%

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

      4. unpow2 89.3%

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

      5. unpow2 89.3%

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

      6. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around inf 98.0%

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

      1. neg-mul-1 98.0%

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

      2. unsub-neg 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in C around 0 98.0%

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

      1. associate-*r/ 98.0%

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

      2. neg-mul-1 98.0%

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

      3. distribute-neg-in 98.0%

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

      4. sub-neg 98.0%

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

      5. div-sub 98.0%

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

      6. distribute-frac-neg 98.0%

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

      7. *-inverses 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. +-commutative 98.0%

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

      11. unsub-neg 98.0%

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

   9. Simplified 98.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9 \cdot 10^{-68}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+178}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 47.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.2e-297)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 3.8e-180)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A 1.5e-69)
       (* 180.0 (/ (atan (/ C B)) PI))
       (if (<= A 1.1e-28)
         (* 180.0 (/ (atan -1.0) PI))
         (* 180.0 (/ (atan (/ (- A) B)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-297) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 3.8e-180) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.5e-69) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (A <= 1.1e-28) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-297) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 3.8e-180) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.5e-69) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (A <= 1.1e-28) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.2e-297:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 3.8e-180:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.5e-69:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif A <= 1.1e-28:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.2e-297)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 3.8e-180)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.5e-69)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (A <= 1.1e-28)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e-297)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 3.8e-180)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.5e-69)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (A <= 1.1e-28)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.2e-297], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-180], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.5e-69], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.1e-28], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.2e-297

   1. Initial program 34.7%

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

      1. associate-*l/ 34.7%

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

      2. *-lft-identity 34.7%

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

      3. +-commutative 34.7%

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

      4. unpow2 34.7%

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

      5. unpow2 34.7%

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

      6. hypot-def 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in A around -inf 54.2%

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

   if -1.2e-297 < A < 3.79999999999999999e-180

   1. Initial program 46.2%

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

      1. associate-*l/ 46.2%

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

      2. *-lft-identity 46.2%

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

      3. +-commutative 46.2%

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

      4. unpow2 46.2%

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

      5. unpow2 46.2%

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

      6. hypot-def 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in B around -inf 33.6%

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

   if 3.79999999999999999e-180 < A < 1.49999999999999995e-69

   1. Initial program 71.5%

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

      1. associate-*l/ 71.5%

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

      2. *-lft-identity 71.5%

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

      3. +-commutative 71.5%

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

      4. unpow2 71.5%

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

      5. unpow2 71.5%

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

      6. hypot-def 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in B around inf 60.5%

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

      1. neg-mul-1 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in C around inf 40.7%

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

   if 1.49999999999999995e-69 < A < 1.09999999999999998e-28

   1. Initial program 65.6%

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

      1. associate-*l/ 65.6%

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

      2. *-lft-identity 65.6%

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

      3. +-commutative 65.6%

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

      4. unpow2 65.6%

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

      5. unpow2 65.6%

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

      6. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around inf 37.6%

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

   if 1.09999999999999998e-28 < A

   1. Initial program 76.0%

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

      1. associate-*l/ 76.0%

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

      2. *-lft-identity 76.0%

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

      3. +-commutative 76.0%

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

      4. unpow2 76.0%

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

      5. unpow2 76.0%

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

      6. hypot-def 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in B around inf 80.1%

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

      1. neg-mul-1 80.1%

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

      2. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in A around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

   9. Simplified 70.3%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 45.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.9 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.1e-197)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7.9e-168)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 6.4e+71)
       (* 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 <= -3.1e-197) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.9e-168) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 6.4e+71) {
		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 <= -3.1e-197) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.9e-168) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 6.4e+71) {
		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 <= -3.1e-197:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.9e-168:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 6.4e+71:
		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 <= -3.1e-197)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.9e-168)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 6.4e+71)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.1e-197)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.9e-168)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 6.4e+71)
		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, -3.1e-197], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.9e-168], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.4e+71], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.10000000000000029e-197

   1. Initial program 49.3%

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

      1. associate-*l/ 49.3%

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

      2. *-lft-identity 49.3%

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

      3. +-commutative 49.3%

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

      4. unpow2 49.3%

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

      5. unpow2 49.3%

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

      6. hypot-def 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in B around -inf 39.4%

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

   if -3.10000000000000029e-197 < B < 7.8999999999999999e-168

   1. Initial program 47.5%

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

      1. associate-*l/ 47.5%

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

      2. *-lft-identity 47.5%

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

      3. +-commutative 47.5%

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

      4. unpow2 47.5%

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

      5. unpow2 47.5%

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

      6. hypot-def 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in C around inf 39.8%

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

      1. distribute-rgt1-in 39.8%

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

      2. metadata-eval 39.8%

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

      3. mul0-lft 39.8%

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

      4. metadata-eval 39.8%

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

   6. Simplified 39.8%

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

   if 7.8999999999999999e-168 < B < 6.40000000000000046e71

   1. Initial program 71.3%

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

      1. associate-*l/ 71.3%

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

      2. *-lft-identity 71.3%

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

      3. +-commutative 71.3%

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

      4. unpow2 71.3%

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

      5. unpow2 71.3%

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

      6. hypot-def 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in B around inf 70.2%

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

      1. neg-mul-1 70.2%

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

      2. unsub-neg 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in A around inf 40.3%

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

      1. associate-*r/ 40.3%

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

      2. mul-1-neg 40.3%

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

   9. Simplified 40.3%

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

   if 6.40000000000000046e71 < B

   1. Initial program 37.6%

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

      1. associate-*l/ 37.6%

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

      2. *-lft-identity 37.6%

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

      3. +-commutative 37.6%

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

      4. unpow2 37.6%

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

      5. unpow2 37.6%

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

      6. hypot-def 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in B around inf 68.9%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.9 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 46.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.1e-197)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.1e-158)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 4.5e+19)
       (* 180.0 (/ (atan (/ C B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.1e-197) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.1e-158) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 4.5e+19) {
		tmp = 180.0 * (atan((C / 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 <= -3.1e-197) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.1e-158) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 4.5e+19) {
		tmp = 180.0 * (Math.atan((C / 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 <= -3.1e-197:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.1e-158:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 4.5e+19:
		tmp = 180.0 * (math.atan((C / 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 <= -3.1e-197)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.1e-158)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 4.5e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(C / 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 <= -3.1e-197)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.1e-158)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 4.5e+19)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.1e-197], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-158], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e+19], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.10000000000000029e-197

   1. Initial program 49.3%

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

      1. associate-*l/ 49.3%

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

      2. *-lft-identity 49.3%

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

      3. +-commutative 49.3%

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

      4. unpow2 49.3%

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

      5. unpow2 49.3%

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

      6. hypot-def 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in B around -inf 39.4%

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

   if -3.10000000000000029e-197 < B < 3.10000000000000018e-158

   1. Initial program 48.6%

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

      1. associate-*l/ 48.6%

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

      2. *-lft-identity 48.6%

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

      3. +-commutative 48.6%

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

      4. unpow2 48.6%

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

      5. unpow2 48.6%

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

      6. hypot-def 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in C around inf 39.0%

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

      1. distribute-rgt1-in 39.0%

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

      2. metadata-eval 39.0%

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

      3. mul0-lft 39.0%

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

      4. metadata-eval 39.0%

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

   6. Simplified 39.0%

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

   if 3.10000000000000018e-158 < B < 4.5e19

   1. Initial program 74.6%

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

      1. associate-*l/ 74.6%

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

      2. *-lft-identity 74.6%

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

      3. +-commutative 74.6%

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

      4. unpow2 74.6%

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

      5. unpow2 74.6%

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

      6. hypot-def 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in B around inf 73.7%

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

      1. neg-mul-1 73.7%

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

      2. unsub-neg 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in C around inf 45.9%

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

   if 4.5e19 < B

   1. Initial program 39.5%

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

      1. associate-*l/ 39.5%

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

      2. *-lft-identity 39.5%

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

      3. +-commutative 39.5%

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

      4. unpow2 39.5%

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

      5. unpow2 39.5%

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

      6. hypot-def 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in B around inf 62.0%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 45.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.1e-197)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.4e-178)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.1e-197) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.4e-178) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.1e-197) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.4e-178) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.1e-197:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.4e-178:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.1e-197)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.4e-178)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.1e-197)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.4e-178)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.1e-197], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-178], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.10000000000000029e-197

   1. Initial program 49.3%

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

      1. associate-*l/ 49.3%

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

      2. *-lft-identity 49.3%

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

      3. +-commutative 49.3%

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

      4. unpow2 49.3%

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

      5. unpow2 49.3%

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

      6. hypot-def 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in B around -inf 39.4%

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

   if -3.10000000000000029e-197 < B < 4.4000000000000002e-178

   1. Initial program 49.5%

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

      1. associate-*l/ 49.5%

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

      2. *-lft-identity 49.5%

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

      3. +-commutative 49.5%

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

      4. unpow2 49.5%

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

      5. unpow2 49.5%

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

      6. hypot-def 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in C around inf 41.4%

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

      1. distribute-rgt1-in 41.4%

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

      2. metadata-eval 41.4%

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

      3. mul0-lft 41.4%

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

      4. metadata-eval 41.4%

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

   6. Simplified 41.4%

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

   if 4.4000000000000002e-178 < B

   1. Initial program 52.5%

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

      1. associate-*l/ 52.5%

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

      2. *-lft-identity 52.5%

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

      3. +-commutative 52.5%

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

      4. unpow2 52.5%

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

      5. unpow2 52.5%

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

      6. hypot-def 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in B around inf 46.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 53.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.3e-300)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.3e-300) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.3e-300) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.3e-300:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.3e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.3e-300)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.3e-300], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.29999999999999998e-300

   1. Initial program 34.4%

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

      1. associate-*l/ 34.4%

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

      2. *-lft-identity 34.4%

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

      3. +-commutative 34.4%

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

      4. unpow2 34.4%

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

      5. unpow2 34.4%

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

      6. hypot-def 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in A around -inf 53.5%

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

   if -1.29999999999999998e-300 < A

   1. Initial program 67.0%

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

      1. associate-*l/ 67.0%

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

      2. *-lft-identity 67.0%

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

      3. +-commutative 67.0%

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

      4. unpow2 67.0%

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

      5. unpow2 67.0%

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

      6. hypot-def 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in B around inf 65.0%

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

      1. neg-mul-1 65.0%

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

      2. unsub-neg 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in C around 0 57.6%

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

      1. associate-*r/ 57.6%

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

      2. neg-mul-1 57.6%

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

      3. distribute-neg-in 57.6%

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

      4. sub-neg 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-frac-neg 57.6%

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

      7. *-inverses 57.6%

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

      8. sub-neg 57.6%

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

      9. metadata-eval 57.6%

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

      10. +-commutative 57.6%

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

      11. unsub-neg 57.6%

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

   9. Simplified 57.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 41.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9e-306) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e-306) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e-306) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9e-306:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9e-306)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9e-306)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9e-306], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.00000000000000009e-306

   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. Step-by-step derivation

      1. associate-*l/ 49.8%

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

      2. *-lft-identity 49.8%

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

      3. +-commutative 49.8%

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

      4. unpow2 49.8%

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

      5. unpow2 49.8%

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

      6. hypot-def 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in B around -inf 34.0%

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

   if -9.00000000000000009e-306 < B

   1. Initial program 51.5%

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

      1. associate-*l/ 51.5%

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

      2. *-lft-identity 51.5%

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

      3. +-commutative 51.5%

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

      4. unpow2 51.5%

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

      5. unpow2 51.5%

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

      6. hypot-def 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in B around inf 40.8%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 21.2% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 50.6%

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

   1. associate-*l/ 50.6%

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

   2. *-lft-identity 50.6%

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

   3. +-commutative 50.6%

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

   4. unpow2 50.6%

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

   5. unpow2 50.6%

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

   6. hypot-def 73.8%

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

3. Simplified 73.8%

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

4. Taylor expanded in B around inf 20.8%

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

5. Final simplification 20.8%

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

Reproduce

herbie shell --seed 2023238 
(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)))