ABCF->ab-angle angle

Percentage Accurate: 54.2% → 81.2%

Time: 19.2s

Alternatives: 19

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: 54.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.2e+83)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+83) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+83) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.2e+83:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.2e+83)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.2e+83)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.2e+83], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $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 < -6.19999999999999984e83

   1. Initial program 18.1%

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

      1. associate-*l/ 18.1%

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

      2. *-lft-identity 18.1%

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

      3. +-commutative 18.1%

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

      4. unpow2 18.1%

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

      5. unpow2 18.1%

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

      6. hypot-def 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in A around -inf 77.4%

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

      1. distribute-lft-out 77.4%

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

      2. *-commutative 77.4%

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

      3. unpow2 77.4%

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

      4. times-frac 81.8%

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

   6. Simplified 81.8%

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

   if -6.19999999999999984e83 < A

   1. Initial program 61.0%

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

      1. associate-*l/ 61.0%

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

      2. *-lft-identity 61.0%

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

      3. +-commutative 61.0%

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

      4. unpow2 61.0%

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

      5. unpow2 61.0%

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

      6. hypot-def 84.7%

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

   3. Simplified 84.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 78.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.8e+80)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (if (<= A 6.8e-155)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot A B))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+80) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if (A <= 6.8e-155) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(A, B))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+80) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if (A <= 6.8e-155) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(A, B))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e+80:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif A <= 6.8e-155:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(A, B))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif (A <= 6.8e-155)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(A, B))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e+80)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif (A <= 6.8e-155)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(A, B))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.8e+80], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.8e-155], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.79999999999999997e80

   1. Initial program 22.0%

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

      1. associate-*l/ 22.0%

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

      2. *-lft-identity 22.0%

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

      3. +-commutative 22.0%

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

      4. unpow2 22.0%

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

      5. unpow2 22.0%

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

      6. hypot-def 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in A around -inf 76.6%

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

      1. distribute-lft-out 76.6%

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

      2. *-commutative 76.6%

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

      3. unpow2 76.6%

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

      4. times-frac 80.8%

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

   6. Simplified 80.8%

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

   if -3.79999999999999997e80 < A < 6.8e-155

   1. Initial program 47.2%

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

      1. associate-*r/ 47.2%

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

      2. associate-*l/ 47.2%

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

      3. associate-*l/ 47.2%

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

      4. *-lft-identity 47.2%

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

      5. sub-neg 47.2%

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

      6. associate-+l- 46.0%

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

      7. sub-neg 46.0%

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

      8. remove-double-neg 46.0%

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

      9. +-commutative 46.0%

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

      10. unpow2 46.0%

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

      11. unpow2 46.0%

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

      12. hypot-def 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in A around 0 46.9%

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

      1. unpow2 46.9%

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

      2. unpow2 46.9%

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

      3. hypot-def 75.9%

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

   6. Simplified 75.9%

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

   if 6.8e-155 < A

   1. Initial program 75.4%

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

      1. associate-*r/ 75.4%

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

      2. associate-*l/ 75.4%

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

      3. associate-*l/ 75.4%

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

      4. *-lft-identity 75.4%

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

      5. sub-neg 75.4%

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

      6. associate-+l- 75.4%

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

      7. sub-neg 75.4%

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

      8. remove-double-neg 75.4%

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

      9. +-commutative 75.4%

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

      10. unpow2 75.4%

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

      11. unpow2 75.4%

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

      12. hypot-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in C around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. unpow2 73.4%

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

      4. hypot-def 90.3%

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

   6. Simplified 90.3%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \]

Alternative 3: 77.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.75 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.75e+80)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (if (<= A 6.5e-87)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.75e+80) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if (A <= 6.5e-87) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} 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 <= -3.75e+80) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if (A <= 6.5e-87) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} 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 <= -3.75e+80:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif A <= 6.5e-87:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	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 <= -3.75e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif (A <= 6.5e-87)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	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 <= -3.75e+80)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif (A <= 6.5e-87)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.75e+80], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.5e-87], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(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 < -3.74999999999999997e80

   1. Initial program 22.0%

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

      1. associate-*l/ 22.0%

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

      2. *-lft-identity 22.0%

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

      3. +-commutative 22.0%

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

      4. unpow2 22.0%

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

      5. unpow2 22.0%

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

      6. hypot-def 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in A around -inf 76.6%

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

      1. distribute-lft-out 76.6%

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

      2. *-commutative 76.6%

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

      3. unpow2 76.6%

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

      4. times-frac 80.8%

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

   6. Simplified 80.8%

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

   if -3.74999999999999997e80 < A < 6.5000000000000003e-87

   1. Initial program 51.1%

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

      1. associate-*r/ 51.1%

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

      2. associate-*l/ 51.1%

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

      3. associate-*l/ 51.1%

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

      4. *-lft-identity 51.1%

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

      5. sub-neg 51.1%

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

      6. associate-+l- 50.1%

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

      7. sub-neg 50.1%

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

      8. remove-double-neg 50.1%

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

      9. +-commutative 50.1%

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

      10. unpow2 50.1%

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

      11. unpow2 50.1%

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

      12. hypot-def 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in A around 0 49.6%

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

      1. unpow2 49.6%

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

      2. unpow2 49.6%

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

      3. hypot-def 76.7%

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

   6. Simplified 76.7%

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

   if 6.5000000000000003e-87 < 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 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in C around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. unpow2 73.2%

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

      4. unpow2 73.2%

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

      5. hypot-def 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.75 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 77.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.25 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.25e+80)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (if (<= A 1.8e-89)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (/ (* 180.0 (atan (/ (- (- A) (hypot A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.25e+80) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if (A <= 1.8e-89) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} 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 <= -2.25e+80) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if (A <= 1.8e-89) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} 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 <= -2.25e+80:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif A <= 1.8e-89:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	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 <= -2.25e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif (A <= 1.8e-89)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 * 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 <= -2.25e+80)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif (A <= 1.8e-89)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 * atan(((-A - hypot(A, B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.25e+80], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.8e-89], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.25000000000000003e80

   1. Initial program 22.0%

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

      1. associate-*l/ 22.0%

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

      2. *-lft-identity 22.0%

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

      3. +-commutative 22.0%

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

      4. unpow2 22.0%

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

      5. unpow2 22.0%

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

      6. hypot-def 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in A around -inf 76.6%

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

      1. distribute-lft-out 76.6%

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

      2. *-commutative 76.6%

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

      3. unpow2 76.6%

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

      4. times-frac 80.8%

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

   6. Simplified 80.8%

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

   if -2.25000000000000003e80 < A < 1.80000000000000003e-89

   1. Initial program 51.1%

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

      1. associate-*r/ 51.1%

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

      2. associate-*l/ 51.1%

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

      3. associate-*l/ 51.1%

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

      4. *-lft-identity 51.1%

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

      5. sub-neg 51.1%

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

      6. associate-+l- 50.1%

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

      7. sub-neg 50.1%

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

      8. remove-double-neg 50.1%

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

      9. +-commutative 50.1%

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

      10. unpow2 50.1%

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

      11. unpow2 50.1%

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

      12. hypot-def 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in A around 0 49.6%

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

      1. unpow2 49.6%

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

      2. unpow2 49.6%

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

      3. hypot-def 76.7%

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

   6. Simplified 76.7%

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

   if 1.80000000000000003e-89 < 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-*r/ 74.4%

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

      2. unpow2 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in C around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. unpow2 73.1%

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

      3. unpow2 73.1%

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

      4. hypot-def 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in C around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. mul-1-neg 73.2%

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

      3. +-commutative 73.2%

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

      4. +-commutative 73.2%

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

      5. unpow2 73.2%

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

      6. unpow2 73.2%

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

      7. hypot-def 90.0%

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

      8. +-commutative 90.0%

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

      9. distribute-neg-in 90.0%

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

      10. sub-neg 90.0%

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

   9. Simplified 90.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.25 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 75.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 310000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e+80)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (if (<= A 310000000000.0)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+80) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if (A <= 310000000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / 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 tmp;
	if (A <= -3.1e+80) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if (A <= 310000000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+80:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif A <= 310000000000.0:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	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 <= -3.1e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif (A <= 310000000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e+80)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif (A <= 310000000000.0)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+80], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 310000000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.09999999999999988e80

   1. Initial program 22.0%

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

      1. associate-*l/ 22.0%

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

      2. *-lft-identity 22.0%

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

      3. +-commutative 22.0%

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

      4. unpow2 22.0%

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

      5. unpow2 22.0%

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

      6. hypot-def 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in A around -inf 76.6%

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

      1. distribute-lft-out 76.6%

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

      2. *-commutative 76.6%

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

      3. unpow2 76.6%

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

      4. times-frac 80.8%

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

   6. Simplified 80.8%

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

   if -3.09999999999999988e80 < A < 3.1e11

   1. Initial program 51.7%

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

      1. associate-*r/ 51.7%

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

      2. associate-*l/ 51.7%

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

      3. associate-*l/ 51.7%

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

      4. *-lft-identity 51.7%

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

      5. sub-neg 51.7%

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

      6. associate-+l- 50.8%

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

      7. sub-neg 50.8%

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

      8. remove-double-neg 50.8%

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

      9. +-commutative 50.8%

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

      10. unpow2 50.8%

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

      11. unpow2 50.8%

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

      12. hypot-def 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in A around 0 49.0%

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

      1. unpow2 49.0%

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

      2. unpow2 49.0%

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

      3. hypot-def 76.8%

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

   6. Simplified 76.8%

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

   if 3.1e11 < A

   1. Initial program 79.1%

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

      1. associate-*r/ 79.1%

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

      2. unpow2 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in C around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. unpow2 77.7%

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

      3. unpow2 77.7%

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

      4. hypot-def 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in C around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. +-commutative 77.7%

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

      3. +-commutative 77.7%

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

      4. unpow2 77.7%

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

      5. unpow2 77.7%

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

      6. hypot-def 91.6%

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

      7. +-commutative 91.6%

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

      8. distribute-neg-in 91.6%

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

      9. sub-neg 91.6%

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

   9. Simplified 91.6%

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

   10. Taylor expanded in B around inf 84.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 310000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.4:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.7 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- C (- A B)) B))))
        (t_1 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= A -3.4)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -5.7e-185)
       t_0
       (if (<= A -8e-230)
         t_1
         (if (<= A 1.4e-287)
           t_0
           (if (<= A 3e-209)
             (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))
             (if (<= A 3.8e-174)
               (/ (* 180.0 (atan (/ (- C B) B))) PI)
               (if (<= A 2.15e-156)
                 t_1
                 (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	double t_1 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (A <= -3.4) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -5.7e-185) {
		tmp = t_0;
	} else if (A <= -8e-230) {
		tmp = t_1;
	} else if (A <= 1.4e-287) {
		tmp = t_0;
	} else if (A <= 3e-209) {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	} else if (A <= 3.8e-174) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (A <= 2.15e-156) {
		tmp = t_1;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	double t_1 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (A <= -3.4) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -5.7e-185) {
		tmp = t_0;
	} else if (A <= -8e-230) {
		tmp = t_1;
	} else if (A <= 1.4e-287) {
		tmp = t_0;
	} else if (A <= 3e-209) {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	} else if (A <= 3.8e-174) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (A <= 2.15e-156) {
		tmp = t_1;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	t_1 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if A <= -3.4:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -5.7e-185:
		tmp = t_0
	elif A <= -8e-230:
		tmp = t_1
	elif A <= 1.4e-287:
		tmp = t_0
	elif A <= 3e-209:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	elif A <= 3.8e-174:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif A <= 2.15e-156:
		tmp = t_1
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)))
	t_1 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (A <= -3.4)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -5.7e-185)
		tmp = t_0;
	elseif (A <= -8e-230)
		tmp = t_1;
	elseif (A <= 1.4e-287)
		tmp = t_0;
	elseif (A <= 3e-209)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	elseif (A <= 3.8e-174)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (A <= 2.15e-156)
		tmp = t_1;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((C - (A - B)) / B));
	t_1 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (A <= -3.4)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -5.7e-185)
		tmp = t_0;
	elseif (A <= -8e-230)
		tmp = t_1;
	elseif (A <= 1.4e-287)
		tmp = t_0;
	elseif (A <= 3e-209)
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	elseif (A <= 3.8e-174)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (A <= 2.15e-156)
		tmp = t_1;
	else
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.4], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -5.7e-185], t$95$0, If[LessEqual[A, -8e-230], t$95$1, If[LessEqual[A, 1.4e-287], t$95$0, If[LessEqual[A, 3e-209], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-174], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.15e-156], t$95$1, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -3.39999999999999991

   1. Initial program 28.2%

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

      1. associate-*r/ 28.3%

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

      2. unpow2 28.3%

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

   3. Simplified 28.3%

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

   4. Taylor expanded in C around 0 26.6%

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

      1. +-commutative 26.6%

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

      2. unpow2 26.6%

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

      3. unpow2 26.6%

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

      4. hypot-def 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in C around 0 25.4%

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

      1. mul-1-neg 25.4%

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

      2. +-commutative 25.4%

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

      3. +-commutative 25.4%

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

      4. unpow2 25.4%

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

      5. unpow2 25.4%

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

      6. hypot-def 47.6%

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

      7. +-commutative 47.6%

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

      8. distribute-neg-in 47.6%

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

      9. sub-neg 47.6%

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

   9. Simplified 47.6%

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

   10. Taylor expanded in A around -inf 71.2%

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

   if -3.39999999999999991 < A < -5.69999999999999986e-185 or -8.00000000000000037e-230 < A < 1.4000000000000001e-287

   1. Initial program 54.3%

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

      1. associate-*r/ 54.2%

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

      2. associate-*l/ 54.3%

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

      3. associate-*l/ 54.3%

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

      4. *-lft-identity 54.3%

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

      5. sub-neg 54.3%

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

      6. associate-+l- 54.1%

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

      7. sub-neg 54.1%

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

      8. remove-double-neg 54.1%

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

      9. +-commutative 54.1%

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

      10. unpow2 54.1%

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

      11. unpow2 54.1%

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

      12. hypot-def 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in B around -inf 60.5%

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

      1. neg-mul-1 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   if -5.69999999999999986e-185 < A < -8.00000000000000037e-230 or 3.80000000000000021e-174 < A < 2.14999999999999989e-156

   1. Initial program 18.8%

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

      1. associate-*l/ 18.8%

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

      2. *-lft-identity 18.8%

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

      3. +-commutative 18.8%

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

      4. unpow2 18.8%

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

      5. unpow2 18.8%

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

      6. hypot-def 31.2%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in C around inf 39.4%

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

      1. fma-def 39.4%

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

      2. associate--l+ 39.4%

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

      3. unpow2 39.4%

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

      4. fma-def 39.4%

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

      5. unpow2 39.4%

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

      6. unpow2 39.4%

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

      7. difference-of-squares 39.4%

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

      8. distribute-rgt1-in 39.4%

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

      9. metadata-eval 39.4%

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

      10. mul0-lft 39.4%

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

      11. mul-1-neg 39.4%

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

      12. distribute-rgt1-in 39.4%

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

      13. metadata-eval 39.4%

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

      14. mul0-lft 39.4%

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

      15. metadata-eval 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in B around 0 70.8%

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

   if 1.4000000000000001e-287 < A < 2.9999999999999999e-209

   1. Initial program 32.6%

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

      1. associate-*l/ 32.6%

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

      2. *-lft-identity 32.6%

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

      3. +-commutative 32.6%

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

      4. unpow2 32.6%

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

      5. unpow2 32.6%

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

      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 C around inf 49.3%

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

      1. fma-def 49.3%

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

      2. associate--l+ 49.3%

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

      3. unpow2 49.3%

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

      4. fma-def 49.3%

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

      5. unpow2 49.3%

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

      6. unpow2 49.3%

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

      7. difference-of-squares 49.3%

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

      8. distribute-rgt1-in 49.3%

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

      9. metadata-eval 49.3%

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

      10. mul0-lft 49.3%

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

      11. mul-1-neg 49.3%

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

      12. distribute-rgt1-in 49.3%

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

      13. metadata-eval 49.3%

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

      14. mul0-lft 49.3%

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

      15. metadata-eval 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in B around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/l* 58.2%

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

   9. Simplified 58.2%

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

   if 2.9999999999999999e-209 < A < 3.80000000000000021e-174

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. unpow2 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in C around 0 52.3%

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

      1. +-commutative 52.3%

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

      2. unpow2 52.3%

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

      3. unpow2 52.3%

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

      4. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in A around 0 70.6%

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

   if 2.14999999999999989e-156 < A

   1. Initial program 75.4%

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

      1. associate-*r/ 75.4%

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

      2. associate-*l/ 75.4%

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

      3. associate-*l/ 75.4%

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

      4. *-lft-identity 75.4%

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

      5. sub-neg 75.4%

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

      6. associate-+l- 75.4%

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

      7. sub-neg 75.4%

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

      8. remove-double-neg 75.4%

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

      9. +-commutative 75.4%

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

      10. unpow2 75.4%

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

      11. unpow2 75.4%

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

      12. hypot-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in B around inf 80.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.7 \cdot 10^{-185}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq -8 \cdot 10^{-230}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 7: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;A \leq -110:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-288}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-172}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- C (- A B)) B))))
        (t_1 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= A -110.0)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -5.5e-185)
       t_0
       (if (<= A -1.25e-224)
         t_1
         (if (<= A 5.8e-288)
           t_0
           (if (<= A 9.5e-212)
             (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))
             (if (<= A 2e-172)
               (/ (* 180.0 (atan (/ (- C B) B))) PI)
               (if (<= A 2.3e-156)
                 t_1
                 (/ (* 180.0 (atan (+ -1.0 (/ (- C A) B)))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	double t_1 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (A <= -110.0) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -5.5e-185) {
		tmp = t_0;
	} else if (A <= -1.25e-224) {
		tmp = t_1;
	} else if (A <= 5.8e-288) {
		tmp = t_0;
	} else if (A <= 9.5e-212) {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	} else if (A <= 2e-172) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (A <= 2.3e-156) {
		tmp = t_1;
	} else {
		tmp = (180.0 * atan((-1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	double t_1 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (A <= -110.0) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -5.5e-185) {
		tmp = t_0;
	} else if (A <= -1.25e-224) {
		tmp = t_1;
	} else if (A <= 5.8e-288) {
		tmp = t_0;
	} else if (A <= 9.5e-212) {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	} else if (A <= 2e-172) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (A <= 2.3e-156) {
		tmp = t_1;
	} else {
		tmp = (180.0 * Math.atan((-1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	t_1 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if A <= -110.0:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -5.5e-185:
		tmp = t_0
	elif A <= -1.25e-224:
		tmp = t_1
	elif A <= 5.8e-288:
		tmp = t_0
	elif A <= 9.5e-212:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	elif A <= 2e-172:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif A <= 2.3e-156:
		tmp = t_1
	else:
		tmp = (180.0 * math.atan((-1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)))
	t_1 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (A <= -110.0)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -5.5e-185)
		tmp = t_0;
	elseif (A <= -1.25e-224)
		tmp = t_1;
	elseif (A <= 5.8e-288)
		tmp = t_0;
	elseif (A <= 9.5e-212)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	elseif (A <= 2e-172)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (A <= 2.3e-156)
		tmp = t_1;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((C - (A - B)) / B));
	t_1 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (A <= -110.0)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -5.5e-185)
		tmp = t_0;
	elseif (A <= -1.25e-224)
		tmp = t_1;
	elseif (A <= 5.8e-288)
		tmp = t_0;
	elseif (A <= 9.5e-212)
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	elseif (A <= 2e-172)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (A <= 2.3e-156)
		tmp = t_1;
	else
		tmp = (180.0 * atan((-1.0 + ((C - 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[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -110.0], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -5.5e-185], t$95$0, If[LessEqual[A, -1.25e-224], t$95$1, If[LessEqual[A, 5.8e-288], t$95$0, If[LessEqual[A, 9.5e-212], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-172], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.3e-156], t$95$1, N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -110

   1. Initial program 28.2%

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

      1. associate-*r/ 28.3%

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

      2. unpow2 28.3%

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

   3. Simplified 28.3%

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

   4. Taylor expanded in C around 0 26.6%

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

      1. +-commutative 26.6%

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

      2. unpow2 26.6%

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

      3. unpow2 26.6%

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

      4. hypot-def 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in C around 0 25.4%

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

      1. mul-1-neg 25.4%

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

      2. +-commutative 25.4%

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

      3. +-commutative 25.4%

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

      4. unpow2 25.4%

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

      5. unpow2 25.4%

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

      6. hypot-def 47.6%

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

      7. +-commutative 47.6%

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

      8. distribute-neg-in 47.6%

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

      9. sub-neg 47.6%

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

   9. Simplified 47.6%

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

   10. Taylor expanded in A around -inf 71.2%

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

   if -110 < A < -5.4999999999999998e-185 or -1.25e-224 < A < 5.8000000000000003e-288

   1. Initial program 54.3%

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

      1. associate-*r/ 54.2%

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

      2. associate-*l/ 54.3%

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

      3. associate-*l/ 54.3%

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

      4. *-lft-identity 54.3%

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

      5. sub-neg 54.3%

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

      6. associate-+l- 54.1%

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

      7. sub-neg 54.1%

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

      8. remove-double-neg 54.1%

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

      9. +-commutative 54.1%

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

      10. unpow2 54.1%

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

      11. unpow2 54.1%

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

      12. hypot-def 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in B around -inf 60.5%

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

      1. neg-mul-1 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   if -5.4999999999999998e-185 < A < -1.25e-224 or 2.0000000000000001e-172 < A < 2.3e-156

   1. Initial program 18.8%

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

      1. associate-*l/ 18.8%

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

      2. *-lft-identity 18.8%

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

      3. +-commutative 18.8%

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

      4. unpow2 18.8%

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

      5. unpow2 18.8%

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

      6. hypot-def 31.2%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in C around inf 39.4%

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

      1. fma-def 39.4%

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

      2. associate--l+ 39.4%

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

      3. unpow2 39.4%

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

      4. fma-def 39.4%

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

      5. unpow2 39.4%

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

      6. unpow2 39.4%

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

      7. difference-of-squares 39.4%

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

      8. distribute-rgt1-in 39.4%

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

      9. metadata-eval 39.4%

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

      10. mul0-lft 39.4%

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

      11. mul-1-neg 39.4%

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

      12. distribute-rgt1-in 39.4%

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

      13. metadata-eval 39.4%

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

      14. mul0-lft 39.4%

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

      15. metadata-eval 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in B around 0 70.8%

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

   if 5.8000000000000003e-288 < A < 9.50000000000000029e-212

   1. Initial program 32.6%

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

      1. associate-*l/ 32.6%

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

      2. *-lft-identity 32.6%

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

      3. +-commutative 32.6%

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

      4. unpow2 32.6%

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

      5. unpow2 32.6%

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

      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 C around inf 49.3%

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

      1. fma-def 49.3%

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

      2. associate--l+ 49.3%

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

      3. unpow2 49.3%

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

      4. fma-def 49.3%

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

      5. unpow2 49.3%

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

      6. unpow2 49.3%

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

      7. difference-of-squares 49.3%

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

      8. distribute-rgt1-in 49.3%

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

      9. metadata-eval 49.3%

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

      10. mul0-lft 49.3%

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

      11. mul-1-neg 49.3%

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

      12. distribute-rgt1-in 49.3%

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

      13. metadata-eval 49.3%

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

      14. mul0-lft 49.3%

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

      15. metadata-eval 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in B around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/l* 58.2%

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

   9. Simplified 58.2%

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

   if 9.50000000000000029e-212 < A < 2.0000000000000001e-172

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. unpow2 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in C around 0 52.3%

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

      1. +-commutative 52.3%

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

      2. unpow2 52.3%

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

      3. unpow2 52.3%

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

      4. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in A around 0 70.6%

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

   if 2.3e-156 < A

   1. Initial program 75.4%

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

      1. associate-*r/ 75.4%

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

      2. unpow2 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in C around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. unpow2 73.4%

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

      4. hypot-def 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in B around inf 78.6%

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

      1. +-commutative 78.6%

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

      2. associate--r+ 78.6%

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

      3. sub-neg 78.6%

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

      4. mul-1-neg 78.6%

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

      5. sub-neg 78.6%

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

      6. metadata-eval 78.6%

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

      7. +-commutative 78.6%

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

      8. mul-1-neg 78.6%

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

      9. sub-neg 78.6%

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

      10. div-sub 80.7%

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

   9. Simplified 80.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -110:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-185}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-172}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 59.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{if}\;A \leq -0.155:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 9.1 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-156}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))))
   (if (<= A -0.155)
     (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
     (if (<= A -3.4e-182)
       t_1
       (if (<= A -9.5e-230)
         t_0
         (if (<= A 1.5e-287)
           t_1
           (if (<= A 9.1e-212)
             (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))
             (if (<= A 6e-174)
               (/ (* 180.0 (atan (/ (- C B) B))) PI)
               (if (<= A 1.05e-156)
                 t_0
                 (/ (* 180.0 (atan (+ -1.0 (/ (- C A) B)))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	double tmp;
	if (A <= -0.155) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if (A <= -3.4e-182) {
		tmp = t_1;
	} else if (A <= -9.5e-230) {
		tmp = t_0;
	} else if (A <= 1.5e-287) {
		tmp = t_1;
	} else if (A <= 9.1e-212) {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	} else if (A <= 6e-174) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (A <= 1.05e-156) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	double tmp;
	if (A <= -0.155) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if (A <= -3.4e-182) {
		tmp = t_1;
	} else if (A <= -9.5e-230) {
		tmp = t_0;
	} else if (A <= 1.5e-287) {
		tmp = t_1;
	} else if (A <= 9.1e-212) {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	} else if (A <= 6e-174) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (A <= 1.05e-156) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	tmp = 0
	if A <= -0.155:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif A <= -3.4e-182:
		tmp = t_1
	elif A <= -9.5e-230:
		tmp = t_0
	elif A <= 1.5e-287:
		tmp = t_1
	elif A <= 9.1e-212:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	elif A <= 6e-174:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif A <= 1.05e-156:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)))
	tmp = 0.0
	if (A <= -0.155)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif (A <= -3.4e-182)
		tmp = t_1;
	elseif (A <= -9.5e-230)
		tmp = t_0;
	elseif (A <= 1.5e-287)
		tmp = t_1;
	elseif (A <= 9.1e-212)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	elseif (A <= 6e-174)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (A <= 1.05e-156)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	t_1 = (180.0 / pi) * atan(((C - (A - B)) / B));
	tmp = 0.0;
	if (A <= -0.155)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif (A <= -3.4e-182)
		tmp = t_1;
	elseif (A <= -9.5e-230)
		tmp = t_0;
	elseif (A <= 1.5e-287)
		tmp = t_1;
	elseif (A <= 9.1e-212)
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	elseif (A <= 6e-174)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (A <= 1.05e-156)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -0.155], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.4e-182], t$95$1, If[LessEqual[A, -9.5e-230], t$95$0, If[LessEqual[A, 1.5e-287], t$95$1, If[LessEqual[A, 9.1e-212], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-174], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.05e-156], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -0.154999999999999999

   1. Initial program 28.2%

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

      1. associate-*l/ 28.2%

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

      2. *-lft-identity 28.2%

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

      3. +-commutative 28.2%

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

      4. unpow2 28.2%

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

      5. unpow2 28.2%

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

      6. hypot-def 54.9%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in A around -inf 68.3%

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

      1. distribute-lft-out 68.3%

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

      2. *-commutative 68.3%

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

      3. unpow2 68.3%

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

      4. times-frac 71.4%

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

   6. Simplified 71.4%

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

   if -0.154999999999999999 < A < -3.39999999999999989e-182 or -9.5000000000000004e-230 < A < 1.49999999999999996e-287

   1. Initial program 54.3%

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

      1. associate-*r/ 54.2%

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

      2. associate-*l/ 54.3%

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

      3. associate-*l/ 54.3%

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

      4. *-lft-identity 54.3%

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

      5. sub-neg 54.3%

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

      6. associate-+l- 54.1%

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

      7. sub-neg 54.1%

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

      8. remove-double-neg 54.1%

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

      9. +-commutative 54.1%

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

      10. unpow2 54.1%

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

      11. unpow2 54.1%

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

      12. hypot-def 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in B around -inf 60.5%

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

      1. neg-mul-1 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   if -3.39999999999999989e-182 < A < -9.5000000000000004e-230 or 6.00000000000000042e-174 < A < 1.05000000000000006e-156

   1. Initial program 18.8%

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

      1. associate-*l/ 18.8%

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

      2. *-lft-identity 18.8%

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

      3. +-commutative 18.8%

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

      4. unpow2 18.8%

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

      5. unpow2 18.8%

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

      6. hypot-def 31.2%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in C around inf 39.4%

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

      1. fma-def 39.4%

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

      2. associate--l+ 39.4%

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

      3. unpow2 39.4%

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

      4. fma-def 39.4%

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

      5. unpow2 39.4%

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

      6. unpow2 39.4%

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

      7. difference-of-squares 39.4%

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

      8. distribute-rgt1-in 39.4%

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

      9. metadata-eval 39.4%

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

      10. mul0-lft 39.4%

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

      11. mul-1-neg 39.4%

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

      12. distribute-rgt1-in 39.4%

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

      13. metadata-eval 39.4%

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

      14. mul0-lft 39.4%

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

      15. metadata-eval 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in B around 0 70.8%

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

   if 1.49999999999999996e-287 < A < 9.1e-212

   1. Initial program 32.6%

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

      1. associate-*l/ 32.6%

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

      2. *-lft-identity 32.6%

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

      3. +-commutative 32.6%

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

      4. unpow2 32.6%

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

      5. unpow2 32.6%

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

      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 C around inf 49.3%

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

      1. fma-def 49.3%

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

      2. associate--l+ 49.3%

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

      3. unpow2 49.3%

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

      4. fma-def 49.3%

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

      5. unpow2 49.3%

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

      6. unpow2 49.3%

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

      7. difference-of-squares 49.3%

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

      8. distribute-rgt1-in 49.3%

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

      9. metadata-eval 49.3%

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

      10. mul0-lft 49.3%

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

      11. mul-1-neg 49.3%

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

      12. distribute-rgt1-in 49.3%

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

      13. metadata-eval 49.3%

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

      14. mul0-lft 49.3%

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

      15. metadata-eval 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in B around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/l* 58.2%

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

   9. Simplified 58.2%

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

   if 9.1e-212 < A < 6.00000000000000042e-174

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. unpow2 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in C around 0 52.3%

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

      1. +-commutative 52.3%

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

      2. unpow2 52.3%

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

      3. unpow2 52.3%

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

      4. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in A around 0 70.6%

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

   if 1.05000000000000006e-156 < A

   1. Initial program 75.4%

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

      1. associate-*r/ 75.4%

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

      2. unpow2 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in C around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. unpow2 73.4%

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

      4. hypot-def 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in B around inf 78.6%

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

      1. +-commutative 78.6%

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

      2. associate--r+ 78.6%

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

      3. sub-neg 78.6%

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

      4. mul-1-neg 78.6%

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

      5. sub-neg 78.6%

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

      6. metadata-eval 78.6%

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

      7. +-commutative 78.6%

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

      8. mul-1-neg 78.6%

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

      9. sub-neg 78.6%

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

      10. div-sub 80.7%

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

   9. Simplified 80.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.155:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-230}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;A \leq 9.1 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;C \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.32 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.9 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.45 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= C -1.05e+28)
     t_0
     (if (<= C -1.32e-56)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (if (<= C -4.9e-164)
         t_0
         (if (<= C 2.45e-247)
           (* 180.0 (/ (atan 1.0) PI))
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (C <= -1.05e+28) {
		tmp = t_0;
	} else if (C <= -1.32e-56) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (C <= -4.9e-164) {
		tmp = t_0;
	} else if (C <= 2.45e-247) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (C <= -1.05e+28) {
		tmp = t_0;
	} else if (C <= -1.32e-56) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (C <= -4.9e-164) {
		tmp = t_0;
	} else if (C <= 2.45e-247) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if C <= -1.05e+28:
		tmp = t_0
	elif C <= -1.32e-56:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif C <= -4.9e-164:
		tmp = t_0
	elif C <= 2.45e-247:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (C <= -1.05e+28)
		tmp = t_0;
	elseif (C <= -1.32e-56)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (C <= -4.9e-164)
		tmp = t_0;
	elseif (C <= 2.45e-247)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (C <= -1.05e+28)
		tmp = t_0;
	elseif (C <= -1.32e-56)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (C <= -4.9e-164)
		tmp = t_0;
	elseif (C <= 2.45e-247)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.05e+28], t$95$0, If[LessEqual[C, -1.32e-56], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -4.9e-164], t$95$0, If[LessEqual[C, 2.45e-247], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.04999999999999995e28 or -1.3199999999999999e-56 < C < -4.8999999999999996e-164

   1. Initial program 80.5%

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

      1. associate-*r/ 80.4%

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

      2. associate-*l/ 80.5%

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

      3. associate-*l/ 80.5%

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

      4. *-lft-identity 80.5%

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

      5. sub-neg 80.5%

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

      6. associate-+l- 80.3%

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

      7. sub-neg 80.3%

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

      8. remove-double-neg 80.3%

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

      9. +-commutative 80.3%

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

      10. unpow2 80.3%

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

      11. unpow2 80.3%

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

      12. hypot-def 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in A around inf 63.8%

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

      1. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in C around inf 61.6%

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

   if -1.04999999999999995e28 < C < -1.3199999999999999e-56

   1. Initial program 45.9%

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

      1. associate-*l/ 45.9%

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

      2. *-lft-identity 45.9%

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

      3. +-commutative 45.9%

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

      4. unpow2 45.9%

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

      5. unpow2 45.9%

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

      6. hypot-def 62.6%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in A around -inf 56.7%

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

   if -4.8999999999999996e-164 < C < 2.45e-247

   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 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in B around -inf 39.7%

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

   if 2.45e-247 < C

   1. Initial program 34.6%

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

      1. associate-*l/ 34.6%

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

      2. *-lft-identity 34.6%

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

      3. +-commutative 34.6%

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

      4. unpow2 34.6%

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

      5. unpow2 34.6%

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

      6. hypot-def 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in C around inf 27.7%

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

      1. fma-def 27.7%

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

      2. associate--l+ 34.1%

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

      3. unpow2 34.1%

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

      4. fma-def 34.1%

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

      5. unpow2 34.1%

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

      6. unpow2 34.1%

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

      7. difference-of-squares 46.9%

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

      8. distribute-rgt1-in 46.9%

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

      9. metadata-eval 46.9%

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

      10. mul0-lft 46.9%

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

      11. mul-1-neg 46.9%

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

      12. distribute-rgt1-in 46.9%

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

      13. metadata-eval 46.9%

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

      14. mul0-lft 46.9%

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

      15. metadata-eval 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in B around 0 52.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq -1.32 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.9 \cdot 10^{-164}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 2.45 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 10: 47.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -7 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.46 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.8 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))))
   (if (<= C -7e+29)
     t_0
     (if (<= C -1.46e-56)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (if (<= C -3.8e-164)
         t_0
         (if (<= C 2.9e-246)
           (* 180.0 (/ (atan 1.0) PI))
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	double tmp;
	if (C <= -7e+29) {
		tmp = t_0;
	} else if (C <= -1.46e-56) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (C <= -3.8e-164) {
		tmp = t_0;
	} else if (C <= 2.9e-246) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	double tmp;
	if (C <= -7e+29) {
		tmp = t_0;
	} else if (C <= -1.46e-56) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (C <= -3.8e-164) {
		tmp = t_0;
	} else if (C <= 2.9e-246) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	tmp = 0
	if C <= -7e+29:
		tmp = t_0
	elif C <= -1.46e-56:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif C <= -3.8e-164:
		tmp = t_0
	elif C <= 2.9e-246:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi))
	tmp = 0.0
	if (C <= -7e+29)
		tmp = t_0;
	elseif (C <= -1.46e-56)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (C <= -3.8e-164)
		tmp = t_0;
	elseif (C <= 2.9e-246)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C * 2.0) / B)) / pi);
	tmp = 0.0;
	if (C <= -7e+29)
		tmp = t_0;
	elseif (C <= -1.46e-56)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (C <= -3.8e-164)
		tmp = t_0;
	elseif (C <= 2.9e-246)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7e+29], t$95$0, If[LessEqual[C, -1.46e-56], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.8e-164], t$95$0, If[LessEqual[C, 2.9e-246], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -6.99999999999999958e29 or -1.46000000000000004e-56 < C < -3.79999999999999989e-164

   1. Initial program 80.5%

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

      1. associate-*l/ 80.5%

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

      2. *-lft-identity 80.5%

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

      3. +-commutative 80.5%

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

      4. unpow2 80.5%

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

      5. unpow2 80.5%

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

      6. hypot-def 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in C around -inf 62.7%

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

   if -6.99999999999999958e29 < C < -1.46000000000000004e-56

   1. Initial program 45.9%

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

      1. associate-*l/ 45.9%

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

      2. *-lft-identity 45.9%

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

      3. +-commutative 45.9%

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

      4. unpow2 45.9%

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

      5. unpow2 45.9%

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

      6. hypot-def 62.6%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in A around -inf 56.7%

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

   if -3.79999999999999989e-164 < C < 2.9e-246

   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 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in B around -inf 39.7%

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

   if 2.9e-246 < C

   1. Initial program 34.6%

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

      1. associate-*l/ 34.6%

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

      2. *-lft-identity 34.6%

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

      3. +-commutative 34.6%

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

      4. unpow2 34.6%

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

      5. unpow2 34.6%

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

      6. hypot-def 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in C around inf 27.7%

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

      1. fma-def 27.7%

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

      2. associate--l+ 34.1%

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

      3. unpow2 34.1%

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

      4. fma-def 34.1%

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

      5. unpow2 34.1%

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

      6. unpow2 34.1%

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

      7. difference-of-squares 46.9%

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

      8. distribute-rgt1-in 46.9%

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

      9. metadata-eval 46.9%

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

      10. mul0-lft 46.9%

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

      11. mul-1-neg 46.9%

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

      12. distribute-rgt1-in 46.9%

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

      13. metadata-eval 46.9%

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

      14. mul0-lft 46.9%

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

      15. metadata-eval 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in B around 0 52.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.46 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.8 \cdot 10^{-164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 11: 56.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -0.0118:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-249}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C B) B))) PI)))
   (if (<= A -0.0118)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -8.5e-164)
       t_0
       (if (<= A 1.65e-249)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= A 6.6e-20) t_0 (/ (* 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) / B))) / ((double) M_PI);
	double tmp;
	if (A <= -0.0118) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -8.5e-164) {
		tmp = t_0;
	} else if (A <= 1.65e-249) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (A <= 6.6e-20) {
		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.atan(((C - B) / B))) / Math.PI;
	double tmp;
	if (A <= -0.0118) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -8.5e-164) {
		tmp = t_0;
	} else if (A <= 1.65e-249) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (A <= 6.6e-20) {
		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.atan(((C - B) / B))) / math.pi
	tmp = 0
	if A <= -0.0118:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -8.5e-164:
		tmp = t_0
	elif A <= 1.65e-249:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif A <= 6.6e-20:
		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 * atan(Float64(Float64(C - B) / B))) / pi)
	tmp = 0.0
	if (A <= -0.0118)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -8.5e-164)
		tmp = t_0;
	elseif (A <= 1.65e-249)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (A <= 6.6e-20)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((C - B) / B))) / pi;
	tmp = 0.0;
	if (A <= -0.0118)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -8.5e-164)
		tmp = t_0;
	elseif (A <= 1.65e-249)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (A <= 6.6e-20)
		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 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[A, -0.0118], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -8.5e-164], t$95$0, If[LessEqual[A, 1.65e-249], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.6e-20], t$95$0, N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -0.0117999999999999997

   1. Initial program 28.1%

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

      1. associate-*r/ 28.1%

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

      2. unpow2 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in C around 0 26.5%

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

      1. +-commutative 26.5%

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

      2. unpow2 26.5%

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

      3. unpow2 26.5%

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

      4. hypot-def 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in C around 0 25.3%

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

      1. mul-1-neg 25.3%

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

      2. +-commutative 25.3%

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

      3. +-commutative 25.3%

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

      4. unpow2 25.3%

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

      5. unpow2 25.3%

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

      6. hypot-def 48.4%

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

      7. +-commutative 48.4%

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

      8. distribute-neg-in 48.4%

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

      9. sub-neg 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in A around -inf 70.4%

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

   if -0.0117999999999999997 < A < -8.50000000000000035e-164 or 1.65e-249 < A < 6.6e-20

   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-*r/ 59.1%

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

      2. unpow2 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in C around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. unpow2 56.5%

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

      3. unpow2 56.5%

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

      4. hypot-def 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in A around 0 55.8%

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

   if -8.50000000000000035e-164 < A < 1.65e-249

   1. Initial program 38.4%

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

      1. associate-*l/ 38.4%

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

      2. *-lft-identity 38.4%

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

      3. +-commutative 38.4%

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

      4. unpow2 38.4%

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

      5. unpow2 38.4%

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

      6. hypot-def 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in C around inf 35.8%

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

      1. fma-def 35.8%

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

      2. associate--l+ 35.8%

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

      3. unpow2 35.8%

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

      4. fma-def 35.8%

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

      5. unpow2 35.8%

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

      6. unpow2 35.8%

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

      7. difference-of-squares 35.8%

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

      8. distribute-rgt1-in 35.8%

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

      9. metadata-eval 35.8%

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

      10. mul0-lft 35.8%

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

      11. mul-1-neg 35.8%

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

      12. distribute-rgt1-in 35.8%

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

      13. metadata-eval 35.8%

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

      14. mul0-lft 35.8%

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

      15. metadata-eval 35.8%

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

   6. Simplified 35.8%

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

   7. Taylor expanded in B around 0 47.9%

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

   if 6.6e-20 < A

   1. Initial program 77.1%

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

      1. associate-*r/ 77.1%

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

      2. unpow2 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in C around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. unpow2 75.6%

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

      3. unpow2 75.6%

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

      4. hypot-def 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in C around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. +-commutative 75.7%

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

      4. unpow2 75.7%

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

      5. unpow2 75.7%

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

      6. hypot-def 89.7%

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

      7. +-commutative 89.7%

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

      8. distribute-neg-in 89.7%

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

      9. sub-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in B around -inf 75.4%

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

       1. mul-1-neg 75.4%

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

       2. unsub-neg 75.4%

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

   12. Simplified 75.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.0118:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-249}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 58.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -0.0115:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -0.0115)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A -1.2e-161)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (if (<= A 1.2e-250)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.0115) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -1.2e-161) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (A <= 1.2e-250) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.0115) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -1.2e-161) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (A <= 1.2e-250) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -0.0115:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -1.2e-161:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif A <= 1.2e-250:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -0.0115)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -1.2e-161)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (A <= 1.2e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -0.0115)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -1.2e-161)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (A <= 1.2e-250)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -0.0115], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.2e-161], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.2e-250], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -0.0115

   1. Initial program 28.1%

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

      1. associate-*r/ 28.1%

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

      2. unpow2 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in C around 0 26.5%

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

      1. +-commutative 26.5%

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

      2. unpow2 26.5%

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

      3. unpow2 26.5%

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

      4. hypot-def 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in C around 0 25.3%

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

      1. mul-1-neg 25.3%

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

      2. +-commutative 25.3%

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

      3. +-commutative 25.3%

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

      4. unpow2 25.3%

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

      5. unpow2 25.3%

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

      6. hypot-def 48.4%

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

      7. +-commutative 48.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\color{blue}{\left(A + \mathsf{hypot}\left(A, B\right)\right)}\right)\right)}{\pi} \]

      8. distribute-neg-in 48.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) + \left(-\mathsf{hypot}\left(A, B\right)\right)\right)}\right)}{\pi} \]

      9. sub-neg 48.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) - \mathsf{hypot}\left(A, B\right)\right)}\right)}{\pi} \]

   9. Simplified 48.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) - \mathsf{hypot}\left(A, B\right)\right)}\right)}{\pi} \]

   10. Taylor expanded in A around -inf 70.4%

       \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -0.0115 < A < -1.19999999999999999e-161

   1. Initial program 59.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 59.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 59.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]

   4. Taylor expanded in C around 0 57.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\sqrt{{B}^{2} + {A}^{2}}}\right)\right)}{\pi} \]
   5. Step-by-step derivation

      1. +-commutative 57.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      2. unpow2 57.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)\right)}{\pi} \]

      3. unpow2 57.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      4. hypot-def 72.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)\right)}{\pi} \]

   6. Simplified 72.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)\right)}{\pi} \]

   7. Taylor expanded in A around 0 49.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - B}{B}\right)}}{\pi} \]

   if -1.19999999999999999e-161 < A < 1.1999999999999999e-250

   1. Initial program 38.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 35.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. fma-def 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi} \]

      2. associate--l+ 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      3. unpow2 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      4. fma-def 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      5. unpow2 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      6. unpow2 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      7. difference-of-squares 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      8. distribute-rgt1-in 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      9. metadata-eval 35.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      10. mul0-lft 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      11. mul-1-neg 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      12. distribute-rgt1-in 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi} \]

      13. metadata-eval 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi} \]

      14. mul0-lft 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi} \]

      15. metadata-eval 35.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi} \]

   6. Simplified 35.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, 0\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 47.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 1.1999999999999999e-250 < A

   1. Initial program 70.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 70.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 70.3%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 70.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 70.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 70.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 90.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around inf 76.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.0115:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 13: 46.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -10000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -10000000.0)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -7e-154)
       t_0
       (if (<= B 3.2e-155)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 7e-12) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -10000000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7e-154) {
		tmp = t_0;
	} else if (B <= 3.2e-155) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 7e-12) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -10000000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7e-154) {
		tmp = t_0;
	} else if (B <= 3.2e-155) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 7e-12) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -10000000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7e-154:
		tmp = t_0
	elif B <= 3.2e-155:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 7e-12:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -10000000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7e-154)
		tmp = t_0;
	elseif (B <= 3.2e-155)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 7e-12)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -10000000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7e-154)
		tmp = t_0;
	elseif (B <= 3.2e-155)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 7e-12)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -10000000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7e-154], t$95$0, If[LessEqual[B, 3.2e-155], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-12], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1e7

   1. Initial program 51.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 51.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 51.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 51.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 51.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 51.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 80.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 63.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1e7 < B < -7.0000000000000001e-154 or 3.20000000000000013e-155 < B < 7.0000000000000001e-12

   1. Initial program 58.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 58.9%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 58.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 58.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 58.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 58.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 58.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 58.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 58.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 58.8%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 58.8%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 64.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 64.1%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in A around inf 54.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{2 \cdot A}}{B}\right) \]
   5. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{A \cdot 2}}{B}\right) \]

   6. Simplified 54.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{A \cdot 2}}{B}\right) \]

   7. Taylor expanded in C around inf 37.9%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if -7.0000000000000001e-154 < B < 3.20000000000000013e-155

   1. Initial program 52.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 52.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 52.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 52.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 52.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 39.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 39.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 39.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 39.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 39.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 39.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 7.0000000000000001e-12 < B

   1. Initial program 50.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 50.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 50.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 50.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 50.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 50.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 84.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 62.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -10000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-154}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-12}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 47.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7.9e-165)
   (* (/ 180.0 PI) (atan (/ C B)))
   (if (<= C 2.05e-247)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.9e-165) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (C <= 2.05e-247) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.9e-165) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (C <= 2.05e-247) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7.9e-165:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif C <= 2.05e-247:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7.9e-165)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (C <= 2.05e-247)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7.9e-165)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (C <= 2.05e-247)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7.9e-165], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e-247], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -7.89999999999999991e-165

   1. Initial program 75.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 75.1%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 75.1%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 75.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 75.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 75.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 75.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 75.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 75.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 75.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 75.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 75.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 83.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in A around inf 58.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{2 \cdot A}}{B}\right) \]
   5. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{A \cdot 2}}{B}\right) \]

   6. Simplified 58.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{A \cdot 2}}{B}\right) \]

   7. Taylor expanded in C around inf 56.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if -7.89999999999999991e-165 < C < 2.0499999999999999e-247

   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 93.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 39.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 2.0499999999999999e-247 < C

   1. Initial program 34.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 34.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 34.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 34.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 34.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 34.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 67.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 27.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. fma-def 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi} \]

      2. associate--l+ 34.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      3. unpow2 34.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      4. fma-def 34.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      5. unpow2 34.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      6. unpow2 34.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      7. difference-of-squares 46.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      8. distribute-rgt1-in 46.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      9. metadata-eval 46.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      10. mul0-lft 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      11. mul-1-neg 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      12. distribute-rgt1-in 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi} \]

      13. metadata-eval 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi} \]

      14. mul0-lft 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi} \]

      15. metadata-eval 46.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi} \]

   6. Simplified 46.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, 0\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 52.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 15: 49.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.6e-119)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 2.15e-154)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e-119) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 2.15e-154) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e-119) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 2.15e-154) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.6e-119:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 2.15e-154:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.6e-119)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 2.15e-154)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.6e-119)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 2.15e-154)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.6e-119], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.15e-154], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.6e-119

   1. Initial program 37.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 63.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 60.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -3.6e-119 < A < 2.14999999999999996e-154

   1. Initial program 42.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 42.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 42.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 42.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 42.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 42.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 75.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 32.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. fma-def 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi} \]

      2. associate--l+ 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      3. unpow2 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      4. fma-def 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      5. unpow2 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      6. unpow2 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      7. difference-of-squares 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      8. distribute-rgt1-in 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      9. metadata-eval 32.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      10. mul0-lft 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      11. mul-1-neg 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      12. distribute-rgt1-in 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi} \]

      13. metadata-eval 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi} \]

      14. mul0-lft 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi} \]

      15. metadata-eval 32.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi} \]

   6. Simplified 32.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, 0\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 42.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 2.14999999999999996e-154 < A

   1. Initial program 75.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 75.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 75.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 75.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 75.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 94.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 94.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around inf 59.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-2 \cdot A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]

   6. Simplified 59.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 53.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.2e-118)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 5e-168)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-118) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 5e-168) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 <= -1.2e-118) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 5e-168) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / 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 <= -1.2e-118:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 5e-168:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / 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 <= -1.2e-118)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 5e-168)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e-118)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 5e-168)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.2e-118], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e-168], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.2000000000000001e-118

   1. Initial program 37.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 37.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 63.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 60.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -1.2000000000000001e-118 < A < 5.00000000000000001e-168

   1. Initial program 43.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 43.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 43.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 43.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 43.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 43.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 76.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 33.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. fma-def 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}{\pi} \]

      2. associate--l+ 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      3. unpow2 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      4. fma-def 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{\mathsf{fma}\left(B, B, {A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      5. unpow2 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      6. unpow2 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, A \cdot A - \color{blue}{\left(-1 \cdot A\right) \cdot \left(-1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      7. difference-of-squares 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(A + -1 \cdot A\right) \cdot \left(A - -1 \cdot A\right)}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      8. distribute-rgt1-in 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      9. metadata-eval 33.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \left(\color{blue}{0} \cdot A\right) \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      10. mul0-lft 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, \color{blue}{0} \cdot \left(A - -1 \cdot A\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      11. mul-1-neg 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \color{blue}{\left(-A\right)}\right)\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}{\pi} \]

      12. distribute-rgt1-in 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}\right)}{B}\right)}{\pi} \]

      13. metadata-eval 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \left(\color{blue}{0} \cdot A\right)\right)}{B}\right)}{\pi} \]

      14. mul0-lft 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, -1 \cdot \color{blue}{0}\right)}{B}\right)}{\pi} \]

      15. metadata-eval 33.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, \color{blue}{0}\right)}{B}\right)}{\pi} \]

   6. Simplified 33.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{C}, 0\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 42.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 5.00000000000000001e-168 < A

   1. Initial program 74.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 74.1%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]

   4. Taylor expanded in C around 0 72.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\sqrt{{B}^{2} + {A}^{2}}}\right)\right)}{\pi} \]
   5. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      2. unpow2 72.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)\right)}{\pi} \]

      3. unpow2 72.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      4. hypot-def 89.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)\right)}{\pi} \]

   6. Simplified 89.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)\right)}{\pi} \]

   7. Taylor expanded in C around 0 69.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(-1 \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)\right)}\right)}{\pi} \]
   8. Step-by-step derivation

      1. mul-1-neg 69.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(-\left(A + \sqrt{{B}^{2} + {A}^{2}}\right)\right)}\right)}{\pi} \]

      2. +-commutative 69.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\color{blue}{\left(\sqrt{{B}^{2} + {A}^{2}} + A\right)}\right)\right)}{\pi} \]

      3. +-commutative 69.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\left(\sqrt{\color{blue}{{A}^{2} + {B}^{2}}} + A\right)\right)\right)}{\pi} \]

      4. unpow2 69.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\left(\sqrt{\color{blue}{A \cdot A} + {B}^{2}} + A\right)\right)\right)}{\pi} \]

      5. unpow2 69.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\left(\sqrt{A \cdot A + \color{blue}{B \cdot B}} + A\right)\right)\right)}{\pi} \]

      6. hypot-def 85.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\left(\color{blue}{\mathsf{hypot}\left(A, B\right)} + A\right)\right)\right)}{\pi} \]

      7. +-commutative 85.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(-\color{blue}{\left(A + \mathsf{hypot}\left(A, B\right)\right)}\right)\right)}{\pi} \]

      8. distribute-neg-in 85.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) + \left(-\mathsf{hypot}\left(A, B\right)\right)\right)}\right)}{\pi} \]

      9. sub-neg 85.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) - \mathsf{hypot}\left(A, B\right)\right)}\right)}{\pi} \]

   9. Simplified 85.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(-A\right) - \mathsf{hypot}\left(A, B\right)\right)}\right)}{\pi} \]

   10. Taylor expanded in B around -inf 66.4%

       \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]
   11. Step-by-step derivation

       1. mul-1-neg 66.4%

          \[\leadsto \frac{180 \cdot \tan^{-1} \left(1 + \color{blue}{\left(-\frac{A}{B}\right)}\right)}{\pi} \]

       2. unsub-neg 66.4%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 - \frac{A}{B}\right)}}{\pi} \]

   12. Simplified 66.4%

       \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(1 - \frac{A}{B}\right)}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 44.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.02 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.02e-70)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.5e-70)
     (* 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 <= -1.02e-70) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.5e-70) {
		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 <= -1.02e-70) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.5e-70) {
		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 <= -1.02e-70:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.5e-70:
		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 <= -1.02e-70)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.5e-70)
		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 <= -1.02e-70)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.5e-70)
		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, -1.02e-70], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e-70], 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 < -1.0200000000000001e-70

   1. Initial program 54.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 78.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 55.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.0200000000000001e-70 < B < 3.49999999999999974e-70

   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 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 31.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 31.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 31.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 31.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 31.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 31.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 3.49999999999999974e-70 < B

   1. Initial program 51.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 51.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 51.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 51.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 51.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 51.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 55.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.02 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18: 40.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 53.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 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 36.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.999999999999994e-310 < B

   1. Initial program 52.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 52.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 52.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 52.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 52.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 78.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 37.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19: 21.0% 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 53.3%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Step-by-step derivation

   1. associate-*l/ 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

   2. *-lft-identity 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

   3. +-commutative 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

   4. unpow2 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

   5. unpow2 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

   6. hypot-def 78.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Simplified 78.4%

   \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

4. Taylor expanded in B around inf 20.7%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

5. Final simplification 20.7%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023176 
(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)))