ABCF->ab-angle angle

Percentage Accurate: 53.8% → 81.7%

Time: 24.1s

Alternatives: 17

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.5e+77)
   (/ (atan (* -0.5 (/ B (- C A)))) (* PI 0.005555555555555556))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.5e+77) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.5e+77) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.5e+77:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.5e+77)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.5e+77)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi * 0.005555555555555556);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.5e+77], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.5e77

   1. Initial program 11.1%

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

   3. Simplified 15.0%

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

   4. Taylor expanded in B around 0 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.5%

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

      4. div-inv 90.5%

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

      5. metadata-eval 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -6.5e77 < A

   1. Initial program 67.9%

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

   3. Simplified 86.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 74.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1 \cdot 10^{+84}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{+187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{C} + 2 \cdot \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))
   (if (<= A -1e+84)
     (/ (atan (* -0.5 (/ B (- C A)))) (* PI 0.005555555555555556))
     (if (<= A 1.1e+66)
       t_0
       (if (<= A 3.9e+148)
         t_1
         (if (<= A 1.95e+187)
           t_0
           (if (<= A 2.8e+213)
             (* 180.0 (/ (atan (+ (/ (* B 0.5) C) (* 2.0 (/ (- C A) B)))) PI))
             t_1)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	double tmp;
	if (A <= -1e+84) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 1.1e+66) {
		tmp = t_0;
	} else if (A <= 3.9e+148) {
		tmp = t_1;
	} else if (A <= 1.95e+187) {
		tmp = t_0;
	} else if (A <= 2.8e+213) {
		tmp = 180.0 * (atan((((B * 0.5) / C) + (2.0 * ((C - A) / B)))) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	double tmp;
	if (A <= -1e+84) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 1.1e+66) {
		tmp = t_0;
	} else if (A <= 3.9e+148) {
		tmp = t_1;
	} else if (A <= 1.95e+187) {
		tmp = t_0;
	} else if (A <= 2.8e+213) {
		tmp = 180.0 * (Math.atan((((B * 0.5) / C) + (2.0 * ((C - A) / B)))) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	tmp = 0
	if A <= -1e+84:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi * 0.005555555555555556)
	elif A <= 1.1e+66:
		tmp = t_0
	elif A <= 3.9e+148:
		tmp = t_1
	elif A <= 1.95e+187:
		tmp = t_0
	elif A <= 2.8e+213:
		tmp = 180.0 * (math.atan((((B * 0.5) / C) + (2.0 * ((C - A) / B)))) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi))
	tmp = 0.0
	if (A <= -1e+84)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 1.1e+66)
		tmp = t_0;
	elseif (A <= 3.9e+148)
		tmp = t_1;
	elseif (A <= 1.95e+187)
		tmp = t_0;
	elseif (A <= 2.8e+213)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B * 0.5) / C) + Float64(2.0 * Float64(Float64(C - A) / B)))) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = 180.0 * (atan((-2.0 * (A / B))) / pi);
	tmp = 0.0;
	if (A <= -1e+84)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi * 0.005555555555555556);
	elseif (A <= 1.1e+66)
		tmp = t_0;
	elseif (A <= 3.9e+148)
		tmp = t_1;
	elseif (A <= 1.95e+187)
		tmp = t_0;
	elseif (A <= 2.8e+213)
		tmp = 180.0 * (atan((((B * 0.5) / C) + (2.0 * ((C - A) / B)))) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1e+84], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.1e+66], t$95$0, If[LessEqual[A, 3.9e+148], t$95$1, If[LessEqual[A, 1.95e+187], t$95$0, If[LessEqual[A, 2.8e+213], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B * 0.5), $MachinePrecision] / C), $MachinePrecision] + N[(2.0 * N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.00000000000000006e84

   1. Initial program 11.1%

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

   3. Simplified 15.0%

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

   4. Taylor expanded in B around 0 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.5%

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

      4. div-inv 90.5%

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

      5. metadata-eval 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -1.00000000000000006e84 < A < 1.0999999999999999e66 or 3.90000000000000002e148 < A < 1.94999999999999991e187

   1. Initial program 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in A around 0 55.2%

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

      1. unpow2 55.2%

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

      2. unpow2 55.2%

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

      3. hypot-def 77.3%

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

   6. Simplified 77.3%

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

   if 1.0999999999999999e66 < A < 3.90000000000000002e148 or 2.7999999999999999e213 < A

   1. Initial program 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in A around inf 87.7%

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

   if 1.94999999999999991e187 < A < 2.7999999999999999e213

   1. Initial program 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in C around -inf 74.1%

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

      1. +-commutative 74.1%

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

      2. +-commutative 74.1%

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

      3. associate-+l+ 74.1%

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

      4. associate-*r/ 74.1%

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

      5. metadata-eval 74.1%

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

      6. cancel-sign-sub-inv 74.1%

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

      7. distribute-lft-out-- 74.1%

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

      8. div-sub 88.4%

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

   6. Simplified 88.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{C} + 2 \cdot \frac{C - A}{B}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+84}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{+148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{+187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{C} + 2 \cdot \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t_1}}\\ \mathbf{elif}\;A \leq -9.6 \cdot 10^{-179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI)))
        (t_1 (atan (* 2.0 (/ C B)))))
   (if (<= A -1.3e-96)
     t_0
     (if (<= A -1.8e-122)
       (/ 180.0 (/ PI t_1))
       (if (<= A -9.6e-179)
         t_0
         (if (<= A -2.3e-266)
           (* 180.0 (/ t_1 PI))
           (if (<= A -6.2e-303)
             (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))
             (if (<= A 1.55e-255)
               (* 180.0 (/ (atan -1.0) PI))
               (if (<= A 6.5e-225)
                 (* 180.0 (/ (atan 1.0) PI))
                 (if (<= A 3e-60)
                   t_0
                   (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	double t_1 = atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.3e-96) {
		tmp = t_0;
	} else if (A <= -1.8e-122) {
		tmp = 180.0 / (((double) M_PI) / t_1);
	} else if (A <= -9.6e-179) {
		tmp = t_0;
	} else if (A <= -2.3e-266) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -6.2e-303) {
		tmp = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	} else if (A <= 1.55e-255) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 6.5e-225) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	double t_1 = Math.atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.3e-96) {
		tmp = t_0;
	} else if (A <= -1.8e-122) {
		tmp = 180.0 / (Math.PI / t_1);
	} else if (A <= -9.6e-179) {
		tmp = t_0;
	} else if (A <= -2.3e-266) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -6.2e-303) {
		tmp = 180.0 * (Math.atan((B / (C / -0.5))) / Math.PI);
	} else if (A <= 1.55e-255) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 6.5e-225) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	t_1 = math.atan((2.0 * (C / B)))
	tmp = 0
	if A <= -1.3e-96:
		tmp = t_0
	elif A <= -1.8e-122:
		tmp = 180.0 / (math.pi / t_1)
	elif A <= -9.6e-179:
		tmp = t_0
	elif A <= -2.3e-266:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -6.2e-303:
		tmp = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	elif A <= 1.55e-255:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 6.5e-225:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3e-60:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi))
	t_1 = atan(Float64(2.0 * Float64(C / B)))
	tmp = 0.0
	if (A <= -1.3e-96)
		tmp = t_0;
	elseif (A <= -1.8e-122)
		tmp = Float64(180.0 / Float64(pi / t_1));
	elseif (A <= -9.6e-179)
		tmp = t_0;
	elseif (A <= -2.3e-266)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -6.2e-303)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi));
	elseif (A <= 1.55e-255)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 6.5e-225)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3e-60)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	t_1 = atan((2.0 * (C / B)));
	tmp = 0.0;
	if (A <= -1.3e-96)
		tmp = t_0;
	elseif (A <= -1.8e-122)
		tmp = 180.0 / (pi / t_1);
	elseif (A <= -9.6e-179)
		tmp = t_0;
	elseif (A <= -2.3e-266)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -6.2e-303)
		tmp = 180.0 * (atan((B / (C / -0.5))) / pi);
	elseif (A <= 1.55e-255)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 6.5e-225)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3e-60)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.3e-96], t$95$0, If[LessEqual[A, -1.8e-122], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9.6e-179], t$95$0, If[LessEqual[A, -2.3e-266], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -6.2e-303], N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.55e-255], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.5e-225], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-60], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if A < -1.3000000000000001e-96 or -1.79999999999999997e-122 < A < -9.6000000000000002e-179 or 6.5000000000000005e-225 < A < 3.00000000000000019e-60

   1. Initial program 30.3%

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

   3. Simplified 47.2%

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

   4. Taylor expanded in B around 0 65.7%

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

   if -1.3000000000000001e-96 < A < -1.79999999999999997e-122

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in C around -inf 57.0%

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

      1. clear-num 57.0%

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

      2. un-div-inv 57.0%

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

   6. Applied egg-rr 57.0%

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

   if -9.6000000000000002e-179 < A < -2.29999999999999996e-266

   1. Initial program 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around -inf 46.2%

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

   if -2.29999999999999996e-266 < A < -6.2000000000000002e-303

   1. Initial program 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in A around 0 55.7%

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

      1. unpow2 55.7%

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

      2. unpow2 55.7%

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

      3. hypot-def 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in C around inf 47.1%

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

      1. associate-*r/ 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-/l* 47.1%

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

   9. Simplified 47.1%

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

   if -6.2000000000000002e-303 < A < 1.54999999999999999e-255

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in B around inf 64.1%

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

   if 1.54999999999999999e-255 < A < 6.5000000000000005e-225

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 3.00000000000000019e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq -9.6 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ t_1 := \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t_1}}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.8 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* -0.5 B) (- C A))) (/ 180.0 PI)))
        (t_1 (atan (* 2.0 (/ C B)))))
   (if (<= A -3.2e-95)
     t_0
     (if (<= A -2.1e-122)
       (/ 180.0 (/ PI t_1))
       (if (<= A -9.2e-179)
         t_0
         (if (<= A -4.8e-266)
           (* 180.0 (/ t_1 PI))
           (if (<= A -2.2e-293)
             (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))
             (if (<= A 2.35e-253)
               (* 180.0 (/ (atan -1.0) PI))
               (if (<= A 1.7e-224)
                 (* 180.0 (/ (atan 1.0) PI))
                 (if (<= A 3.4e-60)
                   (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
                   (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((-0.5 * B) / (C - A))) * (180.0 / ((double) M_PI));
	double t_1 = atan((2.0 * (C / B)));
	double tmp;
	if (A <= -3.2e-95) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 / (((double) M_PI) / t_1);
	} else if (A <= -9.2e-179) {
		tmp = t_0;
	} else if (A <= -4.8e-266) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -2.2e-293) {
		tmp = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	} else if (A <= 2.35e-253) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.7e-224) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3.4e-60) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((-0.5 * B) / (C - A))) * (180.0 / Math.PI);
	double t_1 = Math.atan((2.0 * (C / B)));
	double tmp;
	if (A <= -3.2e-95) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 / (Math.PI / t_1);
	} else if (A <= -9.2e-179) {
		tmp = t_0;
	} else if (A <= -4.8e-266) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -2.2e-293) {
		tmp = 180.0 * (Math.atan((B / (C / -0.5))) / Math.PI);
	} else if (A <= 2.35e-253) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.7e-224) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3.4e-60) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((-0.5 * B) / (C - A))) * (180.0 / math.pi)
	t_1 = math.atan((2.0 * (C / B)))
	tmp = 0
	if A <= -3.2e-95:
		tmp = t_0
	elif A <= -2.1e-122:
		tmp = 180.0 / (math.pi / t_1)
	elif A <= -9.2e-179:
		tmp = t_0
	elif A <= -4.8e-266:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -2.2e-293:
		tmp = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	elif A <= 2.35e-253:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.7e-224:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3.4e-60:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(-0.5 * B) / Float64(C - A))) * Float64(180.0 / pi))
	t_1 = atan(Float64(2.0 * Float64(C / B)))
	tmp = 0.0
	if (A <= -3.2e-95)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = Float64(180.0 / Float64(pi / t_1));
	elseif (A <= -9.2e-179)
		tmp = t_0;
	elseif (A <= -4.8e-266)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -2.2e-293)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi));
	elseif (A <= 2.35e-253)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.7e-224)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3.4e-60)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((-0.5 * B) / (C - A))) * (180.0 / pi);
	t_1 = atan((2.0 * (C / B)));
	tmp = 0.0;
	if (A <= -3.2e-95)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = 180.0 / (pi / t_1);
	elseif (A <= -9.2e-179)
		tmp = t_0;
	elseif (A <= -4.8e-266)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -2.2e-293)
		tmp = 180.0 * (atan((B / (C / -0.5))) / pi);
	elseif (A <= 2.35e-253)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.7e-224)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3.4e-60)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -3.2e-95], t$95$0, If[LessEqual[A, -2.1e-122], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9.2e-179], t$95$0, If[LessEqual[A, -4.8e-266], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.2e-293], N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.35e-253], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.7e-224], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.4e-60], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if A < -3.1999999999999997e-95 or -2.09999999999999992e-122 < A < -9.1999999999999995e-179

   1. Initial program 22.7%

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

   3. Simplified 40.5%

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

   4. Taylor expanded in B around 0 73.8%

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

      1. associate-*r/ 73.8%

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

   6. Applied egg-rr 73.8%

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

   if -3.1999999999999997e-95 < A < -2.09999999999999992e-122

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in C around -inf 57.0%

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

      1. clear-num 57.0%

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

      2. un-div-inv 57.0%

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

   6. Applied egg-rr 57.0%

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

   if -9.1999999999999995e-179 < A < -4.7999999999999999e-266

   1. Initial program 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around -inf 46.2%

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

   if -4.7999999999999999e-266 < A < -2.2e-293

   1. Initial program 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in A around 0 55.7%

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

      1. unpow2 55.7%

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

      2. unpow2 55.7%

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

      3. hypot-def 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in C around inf 47.1%

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

      1. associate-*r/ 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-/l* 47.1%

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

   9. Simplified 47.1%

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

   if -2.2e-293 < A < 2.34999999999999991e-253

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in B around inf 64.1%

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

   if 2.34999999999999991e-253 < A < 1.69999999999999996e-224

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 1.69999999999999996e-224 < A < 3.40000000000000007e-60

   1. Initial program 55.9%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in B around 0 38.5%

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

   if 3.40000000000000007e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -4.8 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ t_1 := \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{t_0}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t_1}}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;t_0 \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B (- C A))))) (t_1 (atan (* 2.0 (/ C B)))))
   (if (<= A -4e-95)
     (/ t_0 (* PI 0.005555555555555556))
     (if (<= A -1.7e-122)
       (/ 180.0 (/ PI t_1))
       (if (<= A -7e-179)
         (* (atan (/ (* -0.5 B) (- C A))) (/ 180.0 PI))
         (if (<= A -2.3e-266)
           (* 180.0 (/ t_1 PI))
           (if (<= A -1.1e-301)
             (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))
             (if (<= A 1.15e-254)
               (* 180.0 (/ (atan -1.0) PI))
               (if (<= A 3.4e-225)
                 (* 180.0 (/ (atan 1.0) PI))
                 (if (<= A 3e-60)
                   (* t_0 (/ 180.0 PI))
                   (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A))));
	double t_1 = atan((2.0 * (C / B)));
	double tmp;
	if (A <= -4e-95) {
		tmp = t_0 / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= -1.7e-122) {
		tmp = 180.0 / (((double) M_PI) / t_1);
	} else if (A <= -7e-179) {
		tmp = atan(((-0.5 * B) / (C - A))) * (180.0 / ((double) M_PI));
	} else if (A <= -2.3e-266) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -1.1e-301) {
		tmp = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	} else if (A <= 1.15e-254) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.4e-225) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3e-60) {
		tmp = t_0 * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A))));
	double t_1 = Math.atan((2.0 * (C / B)));
	double tmp;
	if (A <= -4e-95) {
		tmp = t_0 / (Math.PI * 0.005555555555555556);
	} else if (A <= -1.7e-122) {
		tmp = 180.0 / (Math.PI / t_1);
	} else if (A <= -7e-179) {
		tmp = Math.atan(((-0.5 * B) / (C - A))) * (180.0 / Math.PI);
	} else if (A <= -2.3e-266) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -1.1e-301) {
		tmp = 180.0 * (Math.atan((B / (C / -0.5))) / Math.PI);
	} else if (A <= 1.15e-254) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.4e-225) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3e-60) {
		tmp = t_0 * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A))))
	t_1 = math.atan((2.0 * (C / B)))
	tmp = 0
	if A <= -4e-95:
		tmp = t_0 / (math.pi * 0.005555555555555556)
	elif A <= -1.7e-122:
		tmp = 180.0 / (math.pi / t_1)
	elif A <= -7e-179:
		tmp = math.atan(((-0.5 * B) / (C - A))) * (180.0 / math.pi)
	elif A <= -2.3e-266:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -1.1e-301:
		tmp = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	elif A <= 1.15e-254:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.4e-225:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3e-60:
		tmp = t_0 * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / Float64(C - A))))
	t_1 = atan(Float64(2.0 * Float64(C / B)))
	tmp = 0.0
	if (A <= -4e-95)
		tmp = Float64(t_0 / Float64(pi * 0.005555555555555556));
	elseif (A <= -1.7e-122)
		tmp = Float64(180.0 / Float64(pi / t_1));
	elseif (A <= -7e-179)
		tmp = Float64(atan(Float64(Float64(-0.5 * B) / Float64(C - A))) * Float64(180.0 / pi));
	elseif (A <= -2.3e-266)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -1.1e-301)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi));
	elseif (A <= 1.15e-254)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.4e-225)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3e-60)
		tmp = Float64(t_0 * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A))));
	t_1 = atan((2.0 * (C / B)));
	tmp = 0.0;
	if (A <= -4e-95)
		tmp = t_0 / (pi * 0.005555555555555556);
	elseif (A <= -1.7e-122)
		tmp = 180.0 / (pi / t_1);
	elseif (A <= -7e-179)
		tmp = atan(((-0.5 * B) / (C - A))) * (180.0 / pi);
	elseif (A <= -2.3e-266)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -1.1e-301)
		tmp = 180.0 * (atan((B / (C / -0.5))) / pi);
	elseif (A <= 1.15e-254)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.4e-225)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3e-60)
		tmp = t_0 * (180.0 / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -4e-95], N[(t$95$0 / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.7e-122], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-179], N[(N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.3e-266], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.1e-301], N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.15e-254], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.4e-225], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-60], N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if A < -3.99999999999999996e-95

   1. Initial program 23.1%

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

   3. Simplified 37.3%

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

   4. Taylor expanded in B around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. clear-num 75.5%

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

      3. un-div-inv 75.6%

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

      4. div-inv 75.6%

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

      5. metadata-eval 75.6%

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

   6. Applied egg-rr 75.6%

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

   if -3.99999999999999996e-95 < A < -1.6999999999999999e-122

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in C around -inf 57.0%

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

      1. clear-num 57.0%

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

      2. un-div-inv 57.0%

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

   6. Applied egg-rr 57.0%

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

   if -1.6999999999999999e-122 < A < -7.00000000000000049e-179

   1. Initial program 20.6%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 65.4%

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

      1. associate-*r/ 65.5%

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

   6. Applied egg-rr 65.5%

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

   if -7.00000000000000049e-179 < A < -2.29999999999999996e-266

   1. Initial program 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around -inf 46.2%

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

   if -2.29999999999999996e-266 < A < -1.1e-301

   1. Initial program 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in A around 0 55.7%

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

      1. unpow2 55.7%

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

      2. unpow2 55.7%

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

      3. hypot-def 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in C around inf 47.1%

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

      1. associate-*r/ 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-/l* 47.1%

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

   9. Simplified 47.1%

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

   if -1.1e-301 < A < 1.1499999999999999e-254

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in B around inf 64.1%

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

   if 1.1499999999999999e-254 < A < 3.3999999999999999e-225

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 3.3999999999999999e-225 < A < 3.00000000000000019e-60

   1. Initial program 55.9%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in B around 0 38.5%

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

   if 3.00000000000000019e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 9 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ t_1 := \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{t_0}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t_1}}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-301}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-60}:\\ \;\;\;\;t_0 \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B (- C A))))) (t_1 (atan (* 2.0 (/ C B)))))
   (if (<= A -1.3e-96)
     (/ t_0 (* PI 0.005555555555555556))
     (if (<= A -2e-122)
       (/ 180.0 (/ PI t_1))
       (if (<= A -7e-179)
         (* (atan (/ (* -0.5 B) (- C A))) (/ 180.0 PI))
         (if (<= A -2.9e-266)
           (* 180.0 (/ t_1 PI))
           (if (<= A -6e-301)
             (/ (atan (/ -0.5 (/ (- C A) B))) (* PI 0.005555555555555556))
             (if (<= A 3.05e-254)
               (* 180.0 (/ (atan -1.0) PI))
               (if (<= A 2e-224)
                 (* 180.0 (/ (atan 1.0) PI))
                 (if (<= A 3.8e-60)
                   (* t_0 (/ 180.0 PI))
                   (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A))));
	double t_1 = atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.3e-96) {
		tmp = t_0 / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= -2e-122) {
		tmp = 180.0 / (((double) M_PI) / t_1);
	} else if (A <= -7e-179) {
		tmp = atan(((-0.5 * B) / (C - A))) * (180.0 / ((double) M_PI));
	} else if (A <= -2.9e-266) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -6e-301) {
		tmp = atan((-0.5 / ((C - A) / B))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 3.05e-254) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 2e-224) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3.8e-60) {
		tmp = t_0 * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A))));
	double t_1 = Math.atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.3e-96) {
		tmp = t_0 / (Math.PI * 0.005555555555555556);
	} else if (A <= -2e-122) {
		tmp = 180.0 / (Math.PI / t_1);
	} else if (A <= -7e-179) {
		tmp = Math.atan(((-0.5 * B) / (C - A))) * (180.0 / Math.PI);
	} else if (A <= -2.9e-266) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -6e-301) {
		tmp = Math.atan((-0.5 / ((C - A) / B))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 3.05e-254) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 2e-224) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3.8e-60) {
		tmp = t_0 * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A))))
	t_1 = math.atan((2.0 * (C / B)))
	tmp = 0
	if A <= -1.3e-96:
		tmp = t_0 / (math.pi * 0.005555555555555556)
	elif A <= -2e-122:
		tmp = 180.0 / (math.pi / t_1)
	elif A <= -7e-179:
		tmp = math.atan(((-0.5 * B) / (C - A))) * (180.0 / math.pi)
	elif A <= -2.9e-266:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -6e-301:
		tmp = math.atan((-0.5 / ((C - A) / B))) / (math.pi * 0.005555555555555556)
	elif A <= 3.05e-254:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 2e-224:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3.8e-60:
		tmp = t_0 * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / Float64(C - A))))
	t_1 = atan(Float64(2.0 * Float64(C / B)))
	tmp = 0.0
	if (A <= -1.3e-96)
		tmp = Float64(t_0 / Float64(pi * 0.005555555555555556));
	elseif (A <= -2e-122)
		tmp = Float64(180.0 / Float64(pi / t_1));
	elseif (A <= -7e-179)
		tmp = Float64(atan(Float64(Float64(-0.5 * B) / Float64(C - A))) * Float64(180.0 / pi));
	elseif (A <= -2.9e-266)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -6e-301)
		tmp = Float64(atan(Float64(-0.5 / Float64(Float64(C - A) / B))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 3.05e-254)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 2e-224)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3.8e-60)
		tmp = Float64(t_0 * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A))));
	t_1 = atan((2.0 * (C / B)));
	tmp = 0.0;
	if (A <= -1.3e-96)
		tmp = t_0 / (pi * 0.005555555555555556);
	elseif (A <= -2e-122)
		tmp = 180.0 / (pi / t_1);
	elseif (A <= -7e-179)
		tmp = atan(((-0.5 * B) / (C - A))) * (180.0 / pi);
	elseif (A <= -2.9e-266)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -6e-301)
		tmp = atan((-0.5 / ((C - A) / B))) / (pi * 0.005555555555555556);
	elseif (A <= 3.05e-254)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 2e-224)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3.8e-60)
		tmp = t_0 * (180.0 / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.3e-96], N[(t$95$0 / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-122], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-179], N[(N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.9e-266], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -6e-301], N[(N[ArcTan[N[(-0.5 / N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.05e-254], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-224], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-60], N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if A < -1.3000000000000001e-96

   1. Initial program 23.1%

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

   3. Simplified 37.3%

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

   4. Taylor expanded in B around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. clear-num 75.5%

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

      3. un-div-inv 75.6%

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

      4. div-inv 75.6%

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

      5. metadata-eval 75.6%

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

   6. Applied egg-rr 75.6%

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

   if -1.3000000000000001e-96 < A < -2.00000000000000012e-122

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in C around -inf 57.0%

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

      1. clear-num 57.0%

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

      2. un-div-inv 57.0%

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

   6. Applied egg-rr 57.0%

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

   if -2.00000000000000012e-122 < A < -7.00000000000000049e-179

   1. Initial program 20.6%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 65.4%

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

      1. associate-*r/ 65.5%

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

   6. Applied egg-rr 65.5%

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

   if -7.00000000000000049e-179 < A < -2.89999999999999996e-266

   1. Initial program 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around -inf 46.2%

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

   if -2.89999999999999996e-266 < A < -5.99999999999999998e-301

   1. Initial program 55.7%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in B around 0 46.9%

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

      1. *-commutative 46.9%

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

      2. clear-num 46.9%

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

      3. un-div-inv 46.9%

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

      4. div-inv 46.9%

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

      5. metadata-eval 46.9%

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

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   7. Step-by-step derivation

      1. clear-num 47.1%

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

      2. un-div-inv 47.1%

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

   8. Applied egg-rr 47.1%

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

   if -5.99999999999999998e-301 < A < 3.05e-254

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in B around inf 64.1%

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

   if 3.05e-254 < A < 2e-224

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 2e-224 < A < 3.79999999999999994e-60

   1. Initial program 55.9%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in B around 0 38.5%

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

   if 3.79999999999999994e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 9 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-301}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ t_1 := \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{if}\;A \leq -1.06 \cdot 10^{-95}:\\ \;\;\;\;\frac{t_0}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t_1}}\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-179}:\\ \;\;\;\;t_0 \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (* -0.5 B) (- C A)))) (t_1 (atan (* 2.0 (/ C B)))))
   (if (<= A -1.06e-95)
     (/ t_0 (* PI 0.005555555555555556))
     (if (<= A -1.9e-122)
       (/ 180.0 (/ PI t_1))
       (if (<= A -7.2e-179)
         (* t_0 (/ 180.0 PI))
         (if (<= A -2.8e-266)
           (* 180.0 (/ t_1 PI))
           (if (<= A -8.5e-307)
             (/ (atan (/ -0.5 (/ (- C A) B))) (* PI 0.005555555555555556))
             (if (<= A 2.2e-255)
               (* 180.0 (/ (atan -1.0) PI))
               (if (<= A 1.25e-223)
                 (* 180.0 (/ (atan 1.0) PI))
                 (if (<= A 3.9e-60)
                   (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
                   (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((-0.5 * B) / (C - A)));
	double t_1 = atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.06e-95) {
		tmp = t_0 / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= -1.9e-122) {
		tmp = 180.0 / (((double) M_PI) / t_1);
	} else if (A <= -7.2e-179) {
		tmp = t_0 * (180.0 / ((double) M_PI));
	} else if (A <= -2.8e-266) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -8.5e-307) {
		tmp = atan((-0.5 / ((C - A) / B))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 2.2e-255) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.25e-223) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3.9e-60) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((-0.5 * B) / (C - A)));
	double t_1 = Math.atan((2.0 * (C / B)));
	double tmp;
	if (A <= -1.06e-95) {
		tmp = t_0 / (Math.PI * 0.005555555555555556);
	} else if (A <= -1.9e-122) {
		tmp = 180.0 / (Math.PI / t_1);
	} else if (A <= -7.2e-179) {
		tmp = t_0 * (180.0 / Math.PI);
	} else if (A <= -2.8e-266) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -8.5e-307) {
		tmp = Math.atan((-0.5 / ((C - A) / B))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 2.2e-255) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.25e-223) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3.9e-60) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((-0.5 * B) / (C - A)))
	t_1 = math.atan((2.0 * (C / B)))
	tmp = 0
	if A <= -1.06e-95:
		tmp = t_0 / (math.pi * 0.005555555555555556)
	elif A <= -1.9e-122:
		tmp = 180.0 / (math.pi / t_1)
	elif A <= -7.2e-179:
		tmp = t_0 * (180.0 / math.pi)
	elif A <= -2.8e-266:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -8.5e-307:
		tmp = math.atan((-0.5 / ((C - A) / B))) / (math.pi * 0.005555555555555556)
	elif A <= 2.2e-255:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.25e-223:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3.9e-60:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(-0.5 * B) / Float64(C - A)))
	t_1 = atan(Float64(2.0 * Float64(C / B)))
	tmp = 0.0
	if (A <= -1.06e-95)
		tmp = Float64(t_0 / Float64(pi * 0.005555555555555556));
	elseif (A <= -1.9e-122)
		tmp = Float64(180.0 / Float64(pi / t_1));
	elseif (A <= -7.2e-179)
		tmp = Float64(t_0 * Float64(180.0 / pi));
	elseif (A <= -2.8e-266)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -8.5e-307)
		tmp = Float64(atan(Float64(-0.5 / Float64(Float64(C - A) / B))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 2.2e-255)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.25e-223)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3.9e-60)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((-0.5 * B) / (C - A)));
	t_1 = atan((2.0 * (C / B)));
	tmp = 0.0;
	if (A <= -1.06e-95)
		tmp = t_0 / (pi * 0.005555555555555556);
	elseif (A <= -1.9e-122)
		tmp = 180.0 / (pi / t_1);
	elseif (A <= -7.2e-179)
		tmp = t_0 * (180.0 / pi);
	elseif (A <= -2.8e-266)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -8.5e-307)
		tmp = atan((-0.5 / ((C - A) / B))) / (pi * 0.005555555555555556);
	elseif (A <= 2.2e-255)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.25e-223)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3.9e-60)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.06e-95], N[(t$95$0 / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.9e-122], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7.2e-179], N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.8e-266], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.5e-307], N[(N[ArcTan[N[(-0.5 / N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.2e-255], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-223], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.9e-60], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if A < -1.06e-95

   1. Initial program 23.1%

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

   3. Simplified 37.3%

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

   4. Taylor expanded in B around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. clear-num 75.5%

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

      3. un-div-inv 75.6%

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

      4. div-inv 75.6%

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

      5. metadata-eval 75.6%

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

   6. Applied egg-rr 75.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.5%

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

   8. Applied egg-rr 75.6%

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

   if -1.06e-95 < A < -1.9e-122

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in C around -inf 57.0%

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

      1. clear-num 57.0%

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

      2. un-div-inv 57.0%

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

   6. Applied egg-rr 57.0%

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

   if -1.9e-122 < A < -7.20000000000000015e-179

   1. Initial program 20.6%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 65.4%

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

      1. associate-*r/ 65.5%

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

   6. Applied egg-rr 65.5%

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

   if -7.20000000000000015e-179 < A < -2.8e-266

   1. Initial program 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around -inf 46.2%

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

   if -2.8e-266 < A < -8.4999999999999995e-307

   1. Initial program 55.7%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in B around 0 46.9%

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

      1. *-commutative 46.9%

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

      2. clear-num 46.9%

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

      3. un-div-inv 46.9%

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

      4. div-inv 46.9%

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

      5. metadata-eval 46.9%

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

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   7. Step-by-step derivation

      1. clear-num 47.1%

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

      2. un-div-inv 47.1%

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

   8. Applied egg-rr 47.1%

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

   if -8.4999999999999995e-307 < A < 2.1999999999999999e-255

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in B around inf 64.1%

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

   if 2.1999999999999999e-255 < A < 1.25000000000000006e-223

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 1.25000000000000006e-223 < A < 3.9000000000000002e-60

   1. Initial program 55.9%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in B around 0 38.5%

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

   if 3.9000000000000002e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 9 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{-95}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-179}:\\ \;\;\;\;\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-266}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-60}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 46.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-178}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))))
   (if (<= A -4.8e+76)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A -4.1e-65)
       t_0
       (if (<= A -2.1e-122)
         (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
         (if (<= A -9.5e-178)
           t_0
           (if (<= A 3.5e-252)
             (* 180.0 (/ (atan -1.0) PI))
             (if (<= A 4.2e-225)
               (* 180.0 (/ (atan 1.0) PI))
               (if (<= A 3.2e-60)
                 t_0
                 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	double tmp;
	if (A <= -4.8e+76) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -4.1e-65) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= -9.5e-178) {
		tmp = t_0;
	} else if (A <= 3.5e-252) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 4.2e-225) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3.2e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (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((B / (C / -0.5))) / Math.PI);
	double tmp;
	if (A <= -4.8e+76) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -4.1e-65) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= -9.5e-178) {
		tmp = t_0;
	} else if (A <= 3.5e-252) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 4.2e-225) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3.2e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	tmp = 0
	if A <= -4.8e+76:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -4.1e-65:
		tmp = t_0
	elif A <= -2.1e-122:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= -9.5e-178:
		tmp = t_0
	elif A <= 3.5e-252:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 4.2e-225:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3.2e-60:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi))
	tmp = 0.0
	if (A <= -4.8e+76)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -4.1e-65)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= -9.5e-178)
		tmp = t_0;
	elseif (A <= 3.5e-252)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 4.2e-225)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3.2e-60)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B / (C / -0.5))) / pi);
	tmp = 0.0;
	if (A <= -4.8e+76)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -4.1e-65)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= -9.5e-178)
		tmp = t_0;
	elseif (A <= 3.5e-252)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 4.2e-225)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3.2e-60)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -4.8e+76], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -4.1e-65], t$95$0, If[LessEqual[A, -2.1e-122], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9.5e-178], t$95$0, If[LessEqual[A, 3.5e-252], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.2e-225], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.2e-60], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -4.8e76

   1. Initial program 11.1%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in A around -inf 86.0%

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

      1. associate-*r/ 86.0%

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

   6. Simplified 86.0%

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

   if -4.8e76 < A < -4.09999999999999987e-65 or -2.09999999999999992e-122 < A < -9.50000000000000009e-178 or 4.20000000000000001e-225 < A < 3.2000000000000001e-60

   1. Initial program 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in A around 0 42.4%

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

      1. unpow2 42.4%

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

      2. unpow2 42.4%

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

      3. hypot-def 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in C around inf 43.9%

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

      1. associate-*r/ 43.9%

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

      2. *-commutative 43.9%

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

      3. associate-/l* 43.9%

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

   9. Simplified 43.9%

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

   if -4.09999999999999987e-65 < A < -2.09999999999999992e-122

   1. Initial program 70.1%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in C around -inf 48.2%

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

   if -9.50000000000000009e-178 < A < 3.49999999999999986e-252

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around inf 38.4%

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

   if 3.49999999999999986e-252 < A < 4.20000000000000001e-225

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 3.2000000000000001e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 46.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))))
   (if (<= A -4.8e+76)
     (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
     (if (<= A -1.2e-65)
       t_0
       (if (<= A -1.85e-122)
         (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
         (if (<= A -3.2e-175)
           t_0
           (if (<= A 1.3e-253)
             (* 180.0 (/ (atan -1.0) PI))
             (if (<= A 3.5e-225)
               (* 180.0 (/ (atan 1.0) PI))
               (if (<= A 3e-60)
                 t_0
                 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	double tmp;
	if (A <= -4.8e+76) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= -1.2e-65) {
		tmp = t_0;
	} else if (A <= -1.85e-122) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= -3.2e-175) {
		tmp = t_0;
	} else if (A <= 1.3e-253) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.5e-225) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (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((B / (C / -0.5))) / Math.PI);
	double tmp;
	if (A <= -4.8e+76) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= -1.2e-65) {
		tmp = t_0;
	} else if (A <= -1.85e-122) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= -3.2e-175) {
		tmp = t_0;
	} else if (A <= 1.3e-253) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.5e-225) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	tmp = 0
	if A <= -4.8e+76:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= -1.2e-65:
		tmp = t_0
	elif A <= -1.85e-122:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= -3.2e-175:
		tmp = t_0
	elif A <= 1.3e-253:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.5e-225:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3e-60:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi))
	tmp = 0.0
	if (A <= -4.8e+76)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= -1.2e-65)
		tmp = t_0;
	elseif (A <= -1.85e-122)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= -3.2e-175)
		tmp = t_0;
	elseif (A <= 1.3e-253)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.5e-225)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3e-60)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B / (C / -0.5))) / pi);
	tmp = 0.0;
	if (A <= -4.8e+76)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= -1.2e-65)
		tmp = t_0;
	elseif (A <= -1.85e-122)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= -3.2e-175)
		tmp = t_0;
	elseif (A <= 1.3e-253)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.5e-225)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3e-60)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -4.8e+76], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.2e-65], t$95$0, If[LessEqual[A, -1.85e-122], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.2e-175], t$95$0, If[LessEqual[A, 1.3e-253], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.5e-225], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-60], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -4.8e76

   1. Initial program 11.1%

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

   3. Simplified 15.0%

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

   4. Taylor expanded in B around 0 90.3%

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

   5. Taylor expanded in C around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

   if -4.8e76 < A < -1.2000000000000001e-65 or -1.8499999999999999e-122 < A < -3.2e-175 or 3.4999999999999997e-225 < A < 3.00000000000000019e-60

   1. Initial program 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in A around 0 42.4%

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

      1. unpow2 42.4%

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

      2. unpow2 42.4%

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

      3. hypot-def 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in C around inf 43.9%

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

      1. associate-*r/ 43.9%

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

      2. *-commutative 43.9%

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

      3. associate-/l* 43.9%

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

   9. Simplified 43.9%

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

   if -1.2000000000000001e-65 < A < -1.8499999999999999e-122

   1. Initial program 70.1%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in C around -inf 48.2%

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

   if -3.2e-175 < A < 1.3e-253

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around inf 38.4%

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

   if 1.3e-253 < A < 3.4999999999999997e-225

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 3.00000000000000019e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 46.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{if}\;A \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.55 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ B (/ C -0.5))) PI))))
   (if (<= A -6.2e+76)
     (/ (atan (* 0.5 (/ B A))) (* PI 0.005555555555555556))
     (if (<= A -3.4e-65)
       t_0
       (if (<= A -2.1e-122)
         (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
         (if (<= A -3.7e-178)
           t_0
           (if (<= A 4.55e-256)
             (* 180.0 (/ (atan -1.0) PI))
             (if (<= A 1.55e-225)
               (* 180.0 (/ (atan 1.0) PI))
               (if (<= A 6e-60)
                 t_0
                 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	double tmp;
	if (A <= -6.2e+76) {
		tmp = atan((0.5 * (B / A))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= -3.4e-65) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= -3.7e-178) {
		tmp = t_0;
	} else if (A <= 4.55e-256) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.55e-225) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 6e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (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((B / (C / -0.5))) / Math.PI);
	double tmp;
	if (A <= -6.2e+76) {
		tmp = Math.atan((0.5 * (B / A))) / (Math.PI * 0.005555555555555556);
	} else if (A <= -3.4e-65) {
		tmp = t_0;
	} else if (A <= -2.1e-122) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= -3.7e-178) {
		tmp = t_0;
	} else if (A <= 4.55e-256) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.55e-225) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 6e-60) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	tmp = 0
	if A <= -6.2e+76:
		tmp = math.atan((0.5 * (B / A))) / (math.pi * 0.005555555555555556)
	elif A <= -3.4e-65:
		tmp = t_0
	elif A <= -2.1e-122:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= -3.7e-178:
		tmp = t_0
	elif A <= 4.55e-256:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.55e-225:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 6e-60:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi))
	tmp = 0.0
	if (A <= -6.2e+76)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) / Float64(pi * 0.005555555555555556));
	elseif (A <= -3.4e-65)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= -3.7e-178)
		tmp = t_0;
	elseif (A <= 4.55e-256)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.55e-225)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 6e-60)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B / (C / -0.5))) / pi);
	tmp = 0.0;
	if (A <= -6.2e+76)
		tmp = atan((0.5 * (B / A))) / (pi * 0.005555555555555556);
	elseif (A <= -3.4e-65)
		tmp = t_0;
	elseif (A <= -2.1e-122)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= -3.7e-178)
		tmp = t_0;
	elseif (A <= 4.55e-256)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.55e-225)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 6e-60)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -6.2e+76], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.4e-65], t$95$0, If[LessEqual[A, -2.1e-122], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.7e-178], t$95$0, If[LessEqual[A, 4.55e-256], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.55e-225], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-60], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -6.20000000000000023e76

   1. Initial program 11.1%

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

   3. Simplified 15.0%

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

   4. Taylor expanded in B around 0 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.5%

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

      4. div-inv 90.5%

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

      5. metadata-eval 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in C around 0 86.2%

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

   if -6.20000000000000023e76 < A < -3.39999999999999987e-65 or -2.09999999999999992e-122 < A < -3.70000000000000004e-178 or 1.54999999999999998e-225 < A < 6.00000000000000038e-60

   1. Initial program 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in A around 0 42.4%

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

      1. unpow2 42.4%

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

      2. unpow2 42.4%

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

      3. hypot-def 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in C around inf 43.9%

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

      1. associate-*r/ 43.9%

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

      2. *-commutative 43.9%

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

      3. associate-/l* 43.9%

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

   9. Simplified 43.9%

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

   if -3.39999999999999987e-65 < A < -2.09999999999999992e-122

   1. Initial program 70.1%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in C around -inf 48.2%

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

   if -3.70000000000000004e-178 < A < 4.55e-256

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around inf 38.4%

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

   if 4.55e-256 < A < 1.54999999999999998e-225

   1. Initial program 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in B around -inf 62.6%

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

   if 6.00000000000000038e-60 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.55 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11: 48.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.65 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.3e-50)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C -2.3e-157)
     (* 180.0 (/ (atan -1.0) PI))
     (if (<= C 9.5e-281)
       (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
       (if (<= C 1.65e-239)
         (* 180.0 (/ (atan 1.0) PI))
         (* 180.0 (/ (atan (/ B (/ C -0.5))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.3e-50) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -2.3e-157) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 9.5e-281) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (C <= 1.65e-239) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B / (C / -0.5))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.3e-50) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -2.3e-157) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 9.5e-281) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (C <= 1.65e-239) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B / (C / -0.5))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.3e-50:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -2.3e-157:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 9.5e-281:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif C <= 1.65e-239:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B / (C / -0.5))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.3e-50)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -2.3e-157)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 9.5e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (C <= 1.65e-239)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(C / -0.5))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.3e-50)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -2.3e-157)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 9.5e-281)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (C <= 1.65e-239)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B / (C / -0.5))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.3e-50], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.3e-157], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.5e-281], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.65e-239], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.3000000000000001e-50

   1. Initial program 76.3%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in C around -inf 70.0%

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

   if -1.3000000000000001e-50 < C < -2.29999999999999989e-157

   1. Initial program 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around inf 52.0%

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

   if -2.29999999999999989e-157 < C < 9.5000000000000003e-281

   1. Initial program 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in A around inf 43.7%

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

   if 9.5000000000000003e-281 < C < 1.64999999999999998e-239

   1. Initial program 71.3%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in B around -inf 67.7%

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

   if 1.64999999999999998e-239 < C

   1. Initial program 40.5%

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

   3. Simplified 39.4%

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

   4. Taylor expanded in A around 0 29.0%

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

      1. unpow2 29.0%

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

      2. unpow2 29.0%

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

      3. hypot-def 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in C around inf 51.1%

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

      1. associate-*r/ 51.2%

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

      2. *-commutative 51.2%

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

      3. associate-/l* 51.2%

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

   9. Simplified 51.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C}{-0.5}}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.65 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\pi}\\ \end{array} \]

Alternative 12: 55.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -6.8 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B} + 0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -6.8e-306)
   (* 180.0 (/ (atan (+ (* 2.0 (/ C B)) (* 0.5 (/ B C)))) PI))
   (if (<= C 3.7e-222)
     (* 180.0 (/ (atan 1.0) PI))
     (/ (atan (/ (* -0.5 B) (- C A))) (* PI 0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.8e-306) {
		tmp = 180.0 * (atan(((2.0 * (C / B)) + (0.5 * (B / C)))) / ((double) M_PI));
	} else if (C <= 3.7e-222) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = atan(((-0.5 * B) / (C - A))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.8e-306) {
		tmp = 180.0 * (Math.atan(((2.0 * (C / B)) + (0.5 * (B / C)))) / Math.PI);
	} else if (C <= 3.7e-222) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = Math.atan(((-0.5 * B) / (C - A))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -6.8e-306:
		tmp = 180.0 * (math.atan(((2.0 * (C / B)) + (0.5 * (B / C)))) / math.pi)
	elif C <= 3.7e-222:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = math.atan(((-0.5 * B) / (C - A))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -6.8e-306)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(2.0 * Float64(C / B)) + Float64(0.5 * Float64(B / C)))) / pi));
	elseif (C <= 3.7e-222)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(atan(Float64(Float64(-0.5 * B) / Float64(C - A))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -6.8e-306)
		tmp = 180.0 * (atan(((2.0 * (C / B)) + (0.5 * (B / C)))) / pi);
	elseif (C <= 3.7e-222)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = atan(((-0.5 * B) / (C - A))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -6.8e-306], N[(180.0 * N[(N[ArcTan[N[(N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.7e-222], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.7999999999999996e-306

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in A around 0 62.7%

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

      1. unpow2 62.7%

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

      2. unpow2 62.7%

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

      3. hypot-def 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in C around -inf 63.1%

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

   if -6.7999999999999996e-306 < C < 3.6999999999999999e-222

   1. Initial program 70.3%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in B around -inf 48.4%

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

   if 3.6999999999999999e-222 < C

   1. Initial program 39.5%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in B around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. clear-num 57.6%

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

      3. un-div-inv 57.6%

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

      4. div-inv 57.6%

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

      5. metadata-eval 57.6%

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

   6. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   7. Step-by-step derivation

      1. associate-*r/ 57.6%

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

   8. Applied egg-rr 57.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -6.8 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B} + 0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 13: 45.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{+77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e+47)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -3.5e-128)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= B 4.2e+77)
       (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e+47) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.5e-128) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 4.2e+77) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e+47) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.5e-128) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 4.2e+77) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.8e+47:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.5e-128:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 4.2e+77:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.8e+47)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.5e-128)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 4.2e+77)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.8e+47)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.5e-128)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 4.2e+77)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.8e+47], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.5e-128], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e+77], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.8000000000000003e47

   1. Initial program 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in B around -inf 64.6%

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

   if -3.8000000000000003e47 < B < -3.5e-128

   1. Initial program 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in A around inf 42.6%

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

   if -3.5e-128 < B < 4.1999999999999997e77

   1. Initial program 62.4%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in C around -inf 42.2%

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

   if 4.1999999999999997e77 < B

   1. Initial program 47.2%

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

   3. Simplified 47.2%

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

   4. Taylor expanded in B around inf 64.0%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{+77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 44.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.1e+47)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.6e+101)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e+47) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.6e+101) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e+47) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.6e+101) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.1e+47:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.6e+101:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.1e+47)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.6e+101)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.1e+47)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.6e+101)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.1e+47], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.6e+101], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.1000000000000001e47

   1. Initial program 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in B around -inf 64.6%

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

   if -4.1000000000000001e47 < B < 6.60000000000000022e101

   1. Initial program 65.3%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in A around inf 37.7%

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

   if 6.60000000000000022e101 < B

   1. Initial program 41.8%

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

   3. Simplified 41.8%

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

   4. Taylor expanded in B around inf 67.3%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 45.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.25 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.25e-111)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.5e-93)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.25e-111) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.5e-93) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.25e-111) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.5e-93) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.25e-111:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.5e-93:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.25e-111)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.5e-93)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.25e-111)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.5e-93)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.25e-111], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-93], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.24999999999999987e-111

   1. Initial program 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in B around -inf 48.8%

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

   if -3.24999999999999987e-111 < B < 6.5e-93

   1. Initial program 61.2%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in C around inf 22.0%

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

      1. mul-1-neg 22.0%

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

      2. distribute-rgt1-in 22.0%

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

      3. metadata-eval 22.0%

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

      4. mul0-lft 22.0%

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

      5. distribute-frac-neg 22.0%

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

      6. metadata-eval 22.0%

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

   6. Simplified 22.0%

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

   if 6.5e-93 < B

   1. Initial program 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in B around inf 50.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.25 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 40.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-309) (* 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 <= -1e-309) {
		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 <= -1e-309) {
		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 <= -1e-309:
		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 <= -1e-309)
		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 <= -1e-309)
		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, -1e-309], 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 < -1.000000000000002e-309

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 39.0%

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

   if -1.000000000000002e-309 < B

   1. Initial program 57.2%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in B around inf 37.6%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 21.3% 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 58.6%

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

3. Simplified 58.1%

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

4. Taylor expanded in B around inf 20.4%

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

5. Final simplification 20.4%

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

Reproduce

herbie shell --seed 2023274 
(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)))