ABCF->ab-angle angle

Percentage Accurate: 54.0% → 85.0%

Time: 21.3s

Alternatives: 23

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% 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: 85.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -8.9 \cdot 10^{+111}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- B) (+ C (hypot C B))))))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -8.9e+111)
     (/ (* 180.0 t_1) PI)
     (if (<= A -2.9e+81)
       t_0
       (if (<= A -1.45e-28)
         (* 180.0 (/ t_1 PI))
         (if (<= A 1.8e+72)
           t_0
           (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- A C)))) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-B / (C + hypot(C, B))));
	double t_1 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -8.9e+111) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (A <= -2.9e+81) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= 1.8e+72) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (A - C)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((-B / (C + Math.hypot(C, B))));
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -8.9e+111) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (A <= -2.9e+81) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= 1.8e+72) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-B / (C + math.hypot(C, B))))
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -8.9e+111:
		tmp = (180.0 * t_1) / math.pi
	elif A <= -2.9e+81:
		tmp = t_0
	elif A <= -1.45e-28:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= 1.8e+72:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (A - C)))) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-B) / Float64(C + hypot(C, B)))))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -8.9e+111)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (A <= -2.9e+81)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= 1.8e+72)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-B / (C + hypot(C, B))));
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -8.9e+111)
		tmp = (180.0 * t_1) / pi;
	elseif (A <= -2.9e+81)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= 1.8e+72)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (A - C)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[((-B) / N[(C + N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -8.9e+111], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -2.9e+81], t$95$0, If[LessEqual[A, -1.45e-28], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.8e+72], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -8.89999999999999998e111

   1. Initial program 11.8%

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

      1. associate-*r/ 11.9%

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

      2. unpow2 11.9%

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

   3. Simplified 11.9%

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

      1. associate--l- 11.5%

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

      2. +-commutative 11.5%

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

      3. unpow2 11.5%

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

      4. hypot-udef 25.9%

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

      5. flip-- 10.5%

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

      6. frac-times 5.5%

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

      7. *-un-lft-identity 5.5%

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

      8. pow2 5.5%

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

   5. Applied egg-rr 5.5%

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

      1. associate-+r+ 4.1%

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

   7. Simplified 4.1%

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

   8. Taylor expanded in A around -inf 80.3%

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

   if -8.89999999999999998e111 < A < -2.9e81 or -1.45000000000000006e-28 < A < 1.80000000000000017e72

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. unpow2 55.3%

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

   3. Simplified 55.3%

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

      1. associate--l- 55.4%

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

      2. +-commutative 55.4%

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

      3. unpow2 55.4%

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

      4. hypot-udef 84.3%

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

      5. flip-- 36.0%

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

      6. frac-times 32.2%

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

      7. *-un-lft-identity 32.2%

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

      8. pow2 32.2%

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

   5. Applied egg-rr 32.2%

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

      1. associate-+r+ 32.2%

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

   7. Simplified 32.2%

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

   8. Taylor expanded in A around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. mul-1-neg 53.3%

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

      3. +-commutative 53.3%

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

      4. unpow2 53.3%

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

      5. unpow2 53.3%

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

      6. hypot-def 93.2%

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

   10. Simplified 93.2%

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

       1. *-un-lft-identity 93.2%

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

       2. associate-/l* 92.8%

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

   12. Applied egg-rr 92.8%

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

       1. *-lft-identity 92.8%

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

       2. associate-/r/ 93.2%

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

   14. Simplified 93.2%

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

   if -2.9e81 < A < -1.45000000000000006e-28

   1. Initial program 37.2%

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

      1. associate-*l/ 37.2%

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

      2. *-lft-identity 37.2%

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

      3. +-commutative 37.2%

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

      4. unpow2 37.2%

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

      5. unpow2 37.2%

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

      6. hypot-def 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in A around -inf 64.6%

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

   if 1.80000000000000017e72 < A

   1. Initial program 81.9%

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

      1. associate-*r/ 81.9%

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

      2. associate-*l/ 81.9%

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

      3. associate-*l/ 81.9%

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

      4. *-lft-identity 81.9%

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

      5. sub-neg 81.9%

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

      6. associate-+l- 81.9%

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

      7. sub-neg 81.9%

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

      8. remove-double-neg 81.9%

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

      9. +-commutative 81.9%

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

      10. unpow2 81.9%

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

      11. unpow2 81.9%

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

      12. hypot-def 95.3%

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

   3. Simplified 95.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.9 \cdot 10^{+111}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)\\ \end{array} \]

Alternative 2: 85.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;A \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- B) (+ C (hypot C B))))))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -1.8e+113)
     (/ (* 180.0 t_1) PI)
     (if (<= A -1.65e+81)
       t_0
       (if (<= A -1.45e-28)
         (* 180.0 (/ t_1 PI))
         (if (<= A 2.25e+74)
           t_0
           (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-B / (C + hypot(C, B))));
	double t_1 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.8e+113) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (A <= -1.65e+81) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= 2.25e+74) {
		tmp = t_0;
	} 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 t_0 = (180.0 / Math.PI) * Math.atan((-B / (C + Math.hypot(C, B))));
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.8e+113) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (A <= -1.65e+81) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= 2.25e+74) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-B / (C + math.hypot(C, B))))
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -1.8e+113:
		tmp = (180.0 * t_1) / math.pi
	elif A <= -1.65e+81:
		tmp = t_0
	elif A <= -1.45e-28:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= 2.25e+74:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-B) / Float64(C + hypot(C, B)))))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -1.8e+113)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (A <= -1.65e+81)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= 2.25e+74)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-B / (C + hypot(C, B))));
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -1.8e+113)
		tmp = (180.0 * t_1) / pi;
	elseif (A <= -1.65e+81)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= 2.25e+74)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[((-B) / N[(C + N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.8e+113], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.65e+81], t$95$0, If[LessEqual[A, -1.45e-28], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.25e+74], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.79999999999999996e113

   1. Initial program 11.8%

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

      1. associate-*r/ 11.9%

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

      2. unpow2 11.9%

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

   3. Simplified 11.9%

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

      1. associate--l- 11.5%

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

      2. +-commutative 11.5%

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

      3. unpow2 11.5%

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

      4. hypot-udef 25.9%

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

      5. flip-- 10.5%

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

      6. frac-times 5.5%

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

      7. *-un-lft-identity 5.5%

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

      8. pow2 5.5%

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

   5. Applied egg-rr 5.5%

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

      1. associate-+r+ 4.1%

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

   7. Simplified 4.1%

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

   8. Taylor expanded in A around -inf 80.3%

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

   if -1.79999999999999996e113 < A < -1.65e81 or -1.45000000000000006e-28 < A < 2.25e74

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. unpow2 55.3%

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

   3. Simplified 55.3%

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

      1. associate--l- 55.4%

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

      2. +-commutative 55.4%

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

      3. unpow2 55.4%

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

      4. hypot-udef 84.3%

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

      5. flip-- 36.0%

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

      6. frac-times 32.2%

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

      7. *-un-lft-identity 32.2%

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

      8. pow2 32.2%

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

   5. Applied egg-rr 32.2%

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

      1. associate-+r+ 32.2%

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

   7. Simplified 32.2%

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

   8. Taylor expanded in A around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. mul-1-neg 53.3%

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

      3. +-commutative 53.3%

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

      4. unpow2 53.3%

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

      5. unpow2 53.3%

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

      6. hypot-def 93.2%

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

   10. Simplified 93.2%

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

       1. *-un-lft-identity 93.2%

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

       2. associate-/l* 92.8%

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

   12. Applied egg-rr 92.8%

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

       1. *-lft-identity 92.8%

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

       2. associate-/r/ 93.2%

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

   14. Simplified 93.2%

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

   if -1.65e81 < A < -1.45000000000000006e-28

   1. Initial program 37.2%

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

      1. associate-*l/ 37.2%

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

      2. *-lft-identity 37.2%

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

      3. +-commutative 37.2%

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

      4. unpow2 37.2%

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

      5. unpow2 37.2%

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

      6. hypot-def 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in A around -inf 64.6%

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

   if 2.25e74 < A

   1. Initial program 81.9%

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

      1. associate-*l/ 81.9%

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

      2. *-lft-identity 81.9%

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

      3. +-commutative 81.9%

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

      4. unpow2 81.9%

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

      5. unpow2 81.9%

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

      6. hypot-def 95.3%

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

   3. Simplified 95.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 83.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -7 \cdot 10^{+115}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- B) (+ C (hypot C B))))))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -7e+115)
     (/ (* 180.0 t_1) PI)
     (if (<= A -3.8e+80)
       t_0
       (if (<= A -1.45e-28)
         (* 180.0 (/ t_1 PI))
         (if (<= A 1.25e+147)
           t_0
           (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-B / (C + hypot(C, B))));
	double t_1 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7e+115) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (A <= -3.8e+80) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= 1.25e+147) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((-B / (C + Math.hypot(C, B))));
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7e+115) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (A <= -3.8e+80) {
		tmp = t_0;
	} else if (A <= -1.45e-28) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= 1.25e+147) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-B / (C + math.hypot(C, B))))
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -7e+115:
		tmp = (180.0 * t_1) / math.pi
	elif A <= -3.8e+80:
		tmp = t_0
	elif A <= -1.45e-28:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= 1.25e+147:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-B) / Float64(C + hypot(C, B)))))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -7e+115)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (A <= -3.8e+80)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= 1.25e+147)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-B / (C + hypot(C, B))));
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -7e+115)
		tmp = (180.0 * t_1) / pi;
	elseif (A <= -3.8e+80)
		tmp = t_0;
	elseif (A <= -1.45e-28)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= 1.25e+147)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[((-B) / N[(C + N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -7e+115], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -3.8e+80], t$95$0, If[LessEqual[A, -1.45e-28], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e+147], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7.00000000000000011e115

   1. Initial program 11.8%

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

      1. associate-*r/ 11.9%

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

      2. unpow2 11.9%

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

   3. Simplified 11.9%

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

      1. associate--l- 11.5%

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

      2. +-commutative 11.5%

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

      3. unpow2 11.5%

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

      4. hypot-udef 25.9%

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

      5. flip-- 10.5%

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

      6. frac-times 5.5%

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

      7. *-un-lft-identity 5.5%

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

      8. pow2 5.5%

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

   5. Applied egg-rr 5.5%

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

      1. associate-+r+ 4.1%

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

   7. Simplified 4.1%

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

   8. Taylor expanded in A around -inf 80.3%

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

   if -7.00000000000000011e115 < A < -3.79999999999999997e80 or -1.45000000000000006e-28 < A < 1.2500000000000001e147

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. unpow2 55.3%

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

   3. Simplified 55.3%

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

      1. associate--l- 55.4%

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

      2. +-commutative 55.4%

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

      3. unpow2 55.4%

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

      4. hypot-udef 84.4%

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

      5. flip-- 37.4%

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

      6. frac-times 33.7%

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

      7. *-un-lft-identity 33.7%

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

      8. pow2 33.7%

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

   5. Applied egg-rr 33.7%

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

      1. associate-+r+ 33.6%

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

   7. Simplified 33.6%

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

   8. Taylor expanded in A around 0 51.4%

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

      1. associate-*r/ 51.4%

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

      2. mul-1-neg 51.4%

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

      3. +-commutative 51.4%

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

      4. unpow2 51.4%

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

      5. unpow2 51.4%

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

      6. hypot-def 90.4%

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

   10. Simplified 90.4%

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

       1. *-un-lft-identity 90.4%

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

       2. associate-/l* 90.1%

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

   12. Applied egg-rr 90.1%

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

       1. *-lft-identity 90.1%

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

       2. associate-/r/ 90.4%

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

   14. Simplified 90.4%

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

   if -3.79999999999999997e80 < A < -1.45000000000000006e-28

   1. Initial program 37.2%

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

      1. associate-*l/ 37.2%

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

      2. *-lft-identity 37.2%

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

      3. +-commutative 37.2%

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

      4. unpow2 37.2%

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

      5. unpow2 37.2%

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

      6. hypot-def 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in A around -inf 64.6%

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

   if 1.2500000000000001e147 < A

   1. Initial program 93.9%

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

      1. associate-*l/ 93.9%

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

      2. *-lft-identity 93.9%

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

      3. +-commutative 93.9%

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

      4. unpow2 93.9%

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

      5. unpow2 93.9%

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

      6. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in C around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. unpow2 93.9%

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

      4. unpow2 93.9%

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

      5. hypot-def 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{+115}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{elif}\;A \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{+147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(C, B\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 73.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -5.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.42 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.45 \cdot 10^{+109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot \left(-B\right)}{B \cdot \left(A + \left(C \cdot 2 - A\right)\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -5.5e+108)
     (/ (* 180.0 t_1) PI)
     (if (<= A -5.5e+80)
       t_0
       (if (<= A -1.42e-28)
         (* 180.0 (/ t_1 PI))
         (if (<= A 2.3e+67)
           t_0
           (if (<= A 3.45e+109)
             (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))
             (if (<= A 3.8e+147)
               (/
                (* 180.0 (atan (/ (* B (- B)) (* B (+ A (- (* C 2.0) A))))))
                PI)
               (* 180.0 (/ (atan (/ (- B A) B)) PI))))))))))

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 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -5.5e+108) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (A <= -5.5e+80) {
		tmp = t_0;
	} else if (A <= -1.42e-28) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= 2.3e+67) {
		tmp = t_0;
	} else if (A <= 3.45e+109) {
		tmp = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	} else if (A <= 3.8e+147) {
		tmp = (180.0 * atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -5.5e+108) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (A <= -5.5e+80) {
		tmp = t_0;
	} else if (A <= -1.42e-28) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= 2.3e+67) {
		tmp = t_0;
	} else if (A <= 3.45e+109) {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	} else if (A <= 3.8e+147) {
		tmp = (180.0 * Math.atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -5.5e+108:
		tmp = (180.0 * t_1) / math.pi
	elif A <= -5.5e+80:
		tmp = t_0
	elif A <= -1.42e-28:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= 2.3e+67:
		tmp = t_0
	elif A <= 3.45e+109:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	elif A <= 3.8e+147:
		tmp = (180.0 * math.atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	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 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -5.5e+108)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (A <= -5.5e+80)
		tmp = t_0;
	elseif (A <= -1.42e-28)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= 2.3e+67)
		tmp = t_0;
	elseif (A <= 3.45e+109)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	elseif (A <= 3.8e+147)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * Float64(-B)) / Float64(B * Float64(A + Float64(Float64(C * 2.0) - A)))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	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 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -5.5e+108)
		tmp = (180.0 * t_1) / pi;
	elseif (A <= -5.5e+80)
		tmp = t_0;
	elseif (A <= -1.42e-28)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= 2.3e+67)
		tmp = t_0;
	elseif (A <= 3.45e+109)
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	elseif (A <= 3.8e+147)
		tmp = (180.0 * atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / pi;
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -5.5e+108], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -5.5e+80], t$95$0, If[LessEqual[A, -1.42e-28], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.3e+67], t$95$0, If[LessEqual[A, 3.45e+109], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e+147], N[(N[(180.0 * N[ArcTan[N[(N[(B * (-B)), $MachinePrecision] / N[(B * N[(A + N[(N[(C * 2.0), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -5.4999999999999998e108

   1. Initial program 11.4%

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

      1. associate-*r/ 11.4%

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

      2. unpow2 11.4%

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

   3. Simplified 11.4%

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

      1. associate--l- 11.1%

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

      2. +-commutative 11.1%

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

      3. unpow2 11.1%

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

      4. hypot-udef 24.7%

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

      5. flip-- 10.0%

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

      6. frac-times 5.2%

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

      7. *-un-lft-identity 5.2%

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

      8. pow2 5.2%

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

   5. Applied egg-rr 5.2%

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

      1. associate-+r+ 4.0%

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

   7. Simplified 4.0%

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

   8. Taylor expanded in A around -inf 78.7%

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

   if -5.4999999999999998e108 < A < -5.49999999999999967e80 or -1.42000000000000001e-28 < A < 2.2999999999999999e67

   1. Initial program 56.1%

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

      1. associate-*l/ 56.1%

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

      2. *-lft-identity 56.1%

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

      3. +-commutative 56.1%

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

      4. unpow2 56.1%

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

      5. unpow2 56.1%

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

      6. hypot-def 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in A around 0 53.6%

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

      1. unpow2 53.6%

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

      2. unpow2 53.6%

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

      3. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   if -5.49999999999999967e80 < A < -1.42000000000000001e-28

   1. Initial program 37.2%

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

      1. associate-*l/ 37.2%

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

      2. *-lft-identity 37.2%

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

      3. +-commutative 37.2%

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

      4. unpow2 37.2%

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

      5. unpow2 37.2%

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

      6. hypot-def 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in A around -inf 64.6%

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

   if 2.2999999999999999e67 < A < 3.44999999999999995e109

   1. Initial program 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-lft-identity 71.8%

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

      3. +-commutative 71.8%

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

      4. unpow2 71.8%

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

      5. unpow2 71.8%

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

      6. hypot-def 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in B around inf 89.1%

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

      1. neg-mul-1 89.1%

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

      2. unsub-neg 89.1%

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

   6. Simplified 89.1%

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

   if 3.44999999999999995e109 < A < 3.7999999999999997e147

   1. Initial program 41.5%

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

      1. associate-*r/ 41.5%

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

      2. unpow2 41.5%

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

   3. Simplified 41.5%

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

      1. associate--l- 41.5%

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

      2. +-commutative 41.5%

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

      3. unpow2 41.5%

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

      4. hypot-udef 75.3%

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

      5. flip-- 40.4%

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

      6. frac-times 37.1%

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

      7. *-un-lft-identity 37.1%

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

      8. pow2 37.1%

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

   5. Applied egg-rr 37.1%

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

      1. associate-+r+ 37.1%

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

   7. Simplified 37.1%

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

   8. Taylor expanded in A around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unpow2 50.3%

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

   10. Simplified 50.3%

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

   11. Taylor expanded in C around inf 69.9%

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

       1. mul-1-neg 69.9%

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

       2. unsub-neg 69.9%

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

       3. *-commutative 69.9%

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

   13. Simplified 69.9%

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

   if 3.7999999999999997e147 < A

   1. Initial program 93.9%

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

      1. associate-*l/ 93.9%

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

      2. *-lft-identity 93.9%

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

      3. +-commutative 93.9%

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

      4. unpow2 93.9%

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

      5. unpow2 93.9%

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

      6. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around -inf 97.5%

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

   5. Taylor expanded in C around 0 97.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.42 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.45 \cdot 10^{+109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot \left(-B\right)}{B \cdot \left(A + \left(C \cdot 2 - A\right)\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 77.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.15e+41)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 3.6e+101)
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI))
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.15e+41) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 3.6e+101) {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.15e+41) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 3.6e+101) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.15e+41:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 3.6e+101:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.15e+41)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 3.6e+101)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.15e+41)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 3.6e+101)
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.15e+41], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.6e+101], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.1499999999999999e41

   1. Initial program 76.7%

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

      1. associate-*l/ 76.7%

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

      2. *-lft-identity 76.7%

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

      3. +-commutative 76.7%

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

      4. unpow2 76.7%

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

      5. unpow2 76.7%

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

      6. hypot-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in A around 0 76.8%

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

      1. unpow2 76.8%

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

      2. unpow2 76.8%

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

      3. hypot-def 92.3%

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

   6. Simplified 92.3%

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

   if -1.1499999999999999e41 < C < 3.60000000000000029e101

   1. Initial program 56.9%

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

      1. associate-*l/ 56.9%

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

      2. *-lft-identity 56.9%

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

      3. +-commutative 56.9%

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

      4. unpow2 56.9%

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

      5. unpow2 56.9%

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

      6. hypot-def 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in C around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. +-commutative 54.6%

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

      3. unpow2 54.6%

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

      4. unpow2 54.6%

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

      5. hypot-def 76.6%

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

   6. Simplified 76.6%

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

   if 3.60000000000000029e101 < C

   1. Initial program 16.1%

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

      1. associate-*r/ 16.1%

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

      2. unpow2 16.1%

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

   3. Simplified 16.1%

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

      1. associate--l- 16.1%

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

      2. +-commutative 16.1%

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

      3. unpow2 16.1%

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

      4. hypot-udef 56.8%

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

      5. flip-- 6.2%

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

      6. frac-times 5.3%

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

      7. *-un-lft-identity 5.3%

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

      8. pow2 5.3%

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

   5. Applied egg-rr 5.3%

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

      1. associate-+r+ 5.3%

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

   7. Simplified 5.3%

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

   8. Taylor expanded in A around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. mul-1-neg 55.3%

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

      3. +-commutative 55.3%

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

      4. unpow2 55.3%

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

      5. unpow2 55.3%

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

      6. hypot-def 89.6%

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

   10. Simplified 89.6%

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

       1. *-un-lft-identity 89.6%

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

       2. associate-/l* 88.2%

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

   12. Applied egg-rr 88.2%

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

       1. *-lft-identity 88.2%

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

       2. associate-/r/ 89.6%

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

   14. Simplified 89.6%

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

   15. Taylor expanded in B around 0 82.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 6: 64.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B \cdot \left(-B\right)}{B \cdot \left(A + \left(C \cdot 2 - A\right)\right)}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-189}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (/ (* 180.0 (atan (/ (* B (- B)) (* B (+ A (- (* C 2.0) A)))))) PI)))
   (if (<= B -1.3e-85)
     (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
     (if (<= B -3.3e-165)
       t_0
       (if (<= B -2.4e-189)
         (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
         (if (<= B 5.2e-135)
           (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))
           (if (<= B 9.5e-36)
             t_0
             (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / ((double) M_PI);
	double tmp;
	if (B <= -1.3e-85) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else if (B <= -3.3e-165) {
		tmp = t_0;
	} else if (B <= -2.4e-189) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (B <= 5.2e-135) {
		tmp = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	} else if (B <= 9.5e-36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / Math.PI;
	double tmp;
	if (B <= -1.3e-85) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else if (B <= -3.3e-165) {
		tmp = t_0;
	} else if (B <= -2.4e-189) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (B <= 5.2e-135) {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	} else if (B <= 9.5e-36) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / math.pi
	tmp = 0
	if B <= -1.3e-85:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	elif B <= -3.3e-165:
		tmp = t_0
	elif B <= -2.4e-189:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif B <= 5.2e-135:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	elif B <= 9.5e-36:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B * Float64(-B)) / Float64(B * Float64(A + Float64(Float64(C * 2.0) - A)))))) / pi)
	tmp = 0.0
	if (B <= -1.3e-85)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	elseif (B <= -3.3e-165)
		tmp = t_0;
	elseif (B <= -2.4e-189)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (B <= 5.2e-135)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	elseif (B <= 9.5e-36)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((B * -B) / (B * (A + ((C * 2.0) - A)))))) / pi;
	tmp = 0.0;
	if (B <= -1.3e-85)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	elseif (B <= -3.3e-165)
		tmp = t_0;
	elseif (B <= -2.4e-189)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (B <= 5.2e-135)
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	elseif (B <= 9.5e-36)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(B * (-B)), $MachinePrecision] / N[(B * N[(A + N[(N[(C * 2.0), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -1.3e-85], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.3e-165], t$95$0, If[LessEqual[B, -2.4e-189], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.2e-135], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-36], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.30000000000000006e-85

   1. Initial program 54.7%

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

      1. associate-*r/ 54.7%

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

      2. associate-*l/ 54.7%

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

      3. associate-*l/ 54.7%

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

      4. *-lft-identity 54.7%

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

      5. sub-neg 54.7%

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

      6. associate-+l- 54.7%

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

      7. sub-neg 54.7%

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

      8. remove-double-neg 54.7%

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

      9. +-commutative 54.7%

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

      10. unpow2 54.7%

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

      11. unpow2 54.7%

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

      12. hypot-def 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 75.0%

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

      1. neg-mul-1 75.0%

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

      2. unsub-neg 75.0%

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

   6. Simplified 75.0%

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

   if -1.30000000000000006e-85 < B < -3.2999999999999998e-165 or 5.20000000000000008e-135 < B < 9.5000000000000003e-36

   1. Initial program 41.4%

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

      1. associate-*r/ 41.4%

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

      2. unpow2 41.4%

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

   3. Simplified 41.4%

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

      1. associate--l- 41.8%

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

      2. +-commutative 41.8%

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

      3. unpow2 41.8%

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

      4. hypot-udef 57.4%

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

      5. flip-- 35.8%

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

      6. frac-times 37.7%

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

      7. *-un-lft-identity 37.7%

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

      8. pow2 37.7%

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

   5. Applied egg-rr 37.7%

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

      1. associate-+r+ 37.3%

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

   7. Simplified 37.3%

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

   8. Taylor expanded in A around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unpow2 50.4%

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

   10. Simplified 50.4%

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

   11. Taylor expanded in C around inf 68.3%

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

       1. mul-1-neg 68.3%

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

       2. unsub-neg 68.3%

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

       3. *-commutative 68.3%

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

   13. Simplified 68.3%

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

   if -3.2999999999999998e-165 < B < -2.3999999999999998e-189

   1. Initial program 5.6%

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

      1. associate-*r/ 5.6%

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

      2. unpow2 5.6%

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

   3. Simplified 5.6%

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

      1. associate--l- 4.0%

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

      2. +-commutative 4.0%

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

      3. unpow2 4.0%

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

      4. hypot-udef 19.6%

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

      5. flip-- 4.5%

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

      6. frac-times 2.4%

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

      7. *-un-lft-identity 2.4%

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

      8. pow2 2.4%

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

   5. Applied egg-rr 2.4%

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

      1. associate-+r+ 1.9%

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

   7. Simplified 1.9%

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

   8. Taylor expanded in A around -inf 83.3%

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

   if -2.3999999999999998e-189 < B < 5.20000000000000008e-135

   1. Initial program 63.0%

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

      1. associate-*l/ 63.0%

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

      2. *-lft-identity 63.0%

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

      3. +-commutative 63.0%

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

      4. unpow2 63.0%

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

      5. unpow2 63.0%

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

      6. hypot-def 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in B around inf 61.8%

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

      1. neg-mul-1 61.8%

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

      2. unsub-neg 61.8%

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

   6. Simplified 61.8%

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

   if 9.5000000000000003e-36 < B

   1. Initial program 56.2%

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

      1. associate-*l/ 56.3%

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

      2. *-lft-identity 56.3%

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

      3. +-commutative 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-def 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in B around inf 78.2%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-165}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot \left(-B\right)}{B \cdot \left(A + \left(C \cdot 2 - A\right)\right)}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-189}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot \left(-B\right)}{B \cdot \left(A + \left(C \cdot 2 - A\right)\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]

Alternative 7: 57.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -5.3 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.75 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -5.3e+104)
     t_1
     (if (<= A -1.2e+83)
       t_0
       (if (<= A -5e-30)
         t_1
         (if (<= A -2.9e-176)
           t_0
           (if (<= A 1.1e-153)
             (* 180.0 (/ (atan (/ (+ B C) B)) PI))
             (if (<= A 4000.0)
               t_0
               (if (<= A 1.75e+72)
                 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
                 (* 180.0 (/ (atan (/ (- B A) B)) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -5.3e+104) {
		tmp = t_1;
	} else if (A <= -1.2e+83) {
		tmp = t_0;
	} else if (A <= -5e-30) {
		tmp = t_1;
	} else if (A <= -2.9e-176) {
		tmp = t_0;
	} else if (A <= 1.1e-153) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 1.75e+72) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -5.3e+104) {
		tmp = t_1;
	} else if (A <= -1.2e+83) {
		tmp = t_0;
	} else if (A <= -5e-30) {
		tmp = t_1;
	} else if (A <= -2.9e-176) {
		tmp = t_0;
	} else if (A <= 1.1e-153) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 1.75e+72) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -5.3e+104:
		tmp = t_1
	elif A <= -1.2e+83:
		tmp = t_0
	elif A <= -5e-30:
		tmp = t_1
	elif A <= -2.9e-176:
		tmp = t_0
	elif A <= 1.1e-153:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 4000.0:
		tmp = t_0
	elif A <= 1.75e+72:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -5.3e+104)
		tmp = t_1;
	elseif (A <= -1.2e+83)
		tmp = t_0;
	elseif (A <= -5e-30)
		tmp = t_1;
	elseif (A <= -2.9e-176)
		tmp = t_0;
	elseif (A <= 1.1e-153)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 1.75e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -5.3e+104)
		tmp = t_1;
	elseif (A <= -1.2e+83)
		tmp = t_0;
	elseif (A <= -5e-30)
		tmp = t_1;
	elseif (A <= -2.9e-176)
		tmp = t_0;
	elseif (A <= 1.1e-153)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 1.75e+72)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.3e+104], t$95$1, If[LessEqual[A, -1.2e+83], t$95$0, If[LessEqual[A, -5e-30], t$95$1, If[LessEqual[A, -2.9e-176], t$95$0, If[LessEqual[A, 1.1e-153], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4000.0], t$95$0, If[LessEqual[A, 1.75e+72], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -5.2999999999999999e104 or -1.19999999999999996e83 < A < -4.99999999999999972e-30

   1. Initial program 22.6%

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

      1. associate-*l/ 22.6%

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

      2. *-lft-identity 22.6%

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

      3. +-commutative 22.6%

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

      4. unpow2 22.6%

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

      5. unpow2 22.6%

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

      6. hypot-def 46.8%

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

   3. Simplified 46.8%

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

   4. Taylor expanded in A around -inf 72.3%

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

   if -5.2999999999999999e104 < A < -1.19999999999999996e83 or -4.99999999999999972e-30 < A < -2.90000000000000006e-176 or 1.1e-153 < A < 4e3

   1. Initial program 60.9%

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

      1. associate-*l/ 60.9%

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

      2. *-lft-identity 60.9%

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

      3. +-commutative 60.9%

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

      4. unpow2 60.9%

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

      5. unpow2 60.9%

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

      6. hypot-def 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in A around 0 57.3%

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

      1. unpow2 57.3%

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

      2. unpow2 57.3%

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

      3. hypot-def 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in C around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

   if -2.90000000000000006e-176 < A < 1.1e-153

   1. Initial program 56.9%

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

      1. associate-*l/ 56.9%

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

      2. *-lft-identity 56.9%

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

      3. +-commutative 56.9%

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

      4. unpow2 56.9%

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

      5. unpow2 56.9%

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

      6. hypot-def 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in B around -inf 56.4%

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

   5. Taylor expanded in A around 0 54.7%

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

   if 4e3 < A < 1.75000000000000005e72

   1. Initial program 29.2%

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

      1. associate-*l/ 29.2%

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

      2. *-lft-identity 29.2%

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

      3. +-commutative 29.2%

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

      4. unpow2 29.2%

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

      5. unpow2 29.2%

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

      6. hypot-def 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in A around 0 23.8%

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

      1. unpow2 23.8%

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

      2. unpow2 23.8%

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

      3. hypot-def 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in C around inf 67.4%

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

   if 1.75000000000000005e72 < A

   1. Initial program 81.9%

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

      1. associate-*l/ 81.9%

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

      2. *-lft-identity 81.9%

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

      3. +-commutative 81.9%

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

      4. unpow2 81.9%

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

      5. unpow2 81.9%

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

      6. hypot-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in B around -inf 84.3%

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

   5. Taylor expanded in C around 0 82.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.3 \cdot 10^{+104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{+83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.75 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 57.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -4.8e+104)
     t_1
     (if (<= A -5e+84)
       t_0
       (if (<= A -8.2e-30)
         t_1
         (if (<= A -1.52e-176)
           t_0
           (if (<= A 6.8e-154)
             (* 180.0 (/ (atan (/ (+ B C) B)) PI))
             (if (<= A 4000.0)
               t_0
               (if (<= A 4.2e+76)
                 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
                 (* 180.0 (/ (atan (/ (- B A) B)) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -4.8e+104) {
		tmp = t_1;
	} else if (A <= -5e+84) {
		tmp = t_0;
	} else if (A <= -8.2e-30) {
		tmp = t_1;
	} else if (A <= -1.52e-176) {
		tmp = t_0;
	} else if (A <= 6.8e-154) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 4.2e+76) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -4.8e+104) {
		tmp = t_1;
	} else if (A <= -5e+84) {
		tmp = t_0;
	} else if (A <= -8.2e-30) {
		tmp = t_1;
	} else if (A <= -1.52e-176) {
		tmp = t_0;
	} else if (A <= 6.8e-154) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 4.2e+76) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -4.8e+104:
		tmp = t_1
	elif A <= -5e+84:
		tmp = t_0
	elif A <= -8.2e-30:
		tmp = t_1
	elif A <= -1.52e-176:
		tmp = t_0
	elif A <= 6.8e-154:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 4000.0:
		tmp = t_0
	elif A <= 4.2e+76:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -4.8e+104)
		tmp = t_1;
	elseif (A <= -5e+84)
		tmp = t_0;
	elseif (A <= -8.2e-30)
		tmp = t_1;
	elseif (A <= -1.52e-176)
		tmp = t_0;
	elseif (A <= 6.8e-154)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 4.2e+76)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -4.8e+104)
		tmp = t_1;
	elseif (A <= -5e+84)
		tmp = t_0;
	elseif (A <= -8.2e-30)
		tmp = t_1;
	elseif (A <= -1.52e-176)
		tmp = t_0;
	elseif (A <= 6.8e-154)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 4.2e+76)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -4.8e+104], t$95$1, If[LessEqual[A, -5e+84], t$95$0, If[LessEqual[A, -8.2e-30], t$95$1, If[LessEqual[A, -1.52e-176], t$95$0, If[LessEqual[A, 6.8e-154], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4000.0], t$95$0, If[LessEqual[A, 4.2e+76], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -4.8e104 or -5.0000000000000001e84 < A < -8.2000000000000007e-30

   1. Initial program 22.6%

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

      1. associate-*l/ 22.6%

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

      2. *-lft-identity 22.6%

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

      3. +-commutative 22.6%

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

      4. unpow2 22.6%

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

      5. unpow2 22.6%

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

      6. hypot-def 46.8%

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

   3. Simplified 46.8%

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

   4. Taylor expanded in A around -inf 72.3%

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

   if -4.8e104 < A < -5.0000000000000001e84 or -8.2000000000000007e-30 < A < -1.52000000000000001e-176 or 6.7999999999999997e-154 < A < 4e3

   1. Initial program 60.9%

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

      1. associate-*l/ 60.9%

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

      2. *-lft-identity 60.9%

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

      3. +-commutative 60.9%

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

      4. unpow2 60.9%

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

      5. unpow2 60.9%

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

      6. hypot-def 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in A around 0 57.3%

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

      1. unpow2 57.3%

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

      2. unpow2 57.3%

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

      3. hypot-def 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in C around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

   if -1.52000000000000001e-176 < A < 6.7999999999999997e-154

   1. Initial program 56.9%

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

      1. associate-*l/ 56.9%

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

      2. *-lft-identity 56.9%

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

      3. +-commutative 56.9%

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

      4. unpow2 56.9%

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

      5. unpow2 56.9%

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

      6. hypot-def 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in B around -inf 56.4%

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

   5. Taylor expanded in A around 0 54.7%

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

   if 4e3 < A < 4.20000000000000013e76

   1. Initial program 29.2%

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

      1. associate-*r/ 29.2%

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

      2. unpow2 29.2%

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

   3. Simplified 29.2%

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

      1. associate--l- 29.2%

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

      2. +-commutative 29.2%

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

      3. unpow2 29.2%

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

      4. hypot-udef 74.2%

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

      5. flip-- 19.6%

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

      6. frac-times 18.3%

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

      7. *-un-lft-identity 18.3%

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

      8. pow2 18.3%

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

   5. Applied egg-rr 18.3%

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

      1. associate-+r+ 18.3%

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

   7. Simplified 18.3%

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

   8. Taylor expanded in A around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. mul-1-neg 59.9%

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

      3. +-commutative 59.9%

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

      4. unpow2 59.9%

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

      5. unpow2 59.9%

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

      6. hypot-def 90.0%

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

   10. Simplified 90.0%

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

       1. *-un-lft-identity 90.0%

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

       2. associate-/l* 85.8%

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

   12. Applied egg-rr 85.8%

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

       1. *-lft-identity 85.8%

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

       2. associate-/r/ 90.0%

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

   14. Simplified 90.0%

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

   15. Taylor expanded in B around 0 68.1%

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

   if 4.20000000000000013e76 < A

   1. Initial program 81.9%

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

      1. associate-*l/ 81.9%

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

      2. *-lft-identity 81.9%

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

      3. +-commutative 81.9%

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

      4. unpow2 81.9%

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

      5. unpow2 81.9%

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

      6. hypot-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in B around -inf 84.3%

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

   5. Taylor expanded in C around 0 82.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{+84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.2 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 57.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.8 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.75 \cdot 10^{+73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -7.2e+104)
     t_1
     (if (<= A -1.1e+85)
       t_0
       (if (<= A -2.1e-32)
         t_1
         (if (<= A -1.52e-176)
           t_0
           (if (<= A 9.8e-154)
             (* 180.0 (/ (atan (/ (+ B C) B)) PI))
             (if (<= A 4000.0)
               t_0
               (if (<= A 1.75e+73)
                 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
                 (* (/ 180.0 PI) (atan (/ (- B A) B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -7.2e+104) {
		tmp = t_1;
	} else if (A <= -1.1e+85) {
		tmp = t_0;
	} else if (A <= -2.1e-32) {
		tmp = t_1;
	} else if (A <= -1.52e-176) {
		tmp = t_0;
	} else if (A <= 9.8e-154) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 1.75e+73) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -7.2e+104) {
		tmp = t_1;
	} else if (A <= -1.1e+85) {
		tmp = t_0;
	} else if (A <= -2.1e-32) {
		tmp = t_1;
	} else if (A <= -1.52e-176) {
		tmp = t_0;
	} else if (A <= 9.8e-154) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 4000.0) {
		tmp = t_0;
	} else if (A <= 1.75e+73) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -7.2e+104:
		tmp = t_1
	elif A <= -1.1e+85:
		tmp = t_0
	elif A <= -2.1e-32:
		tmp = t_1
	elif A <= -1.52e-176:
		tmp = t_0
	elif A <= 9.8e-154:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 4000.0:
		tmp = t_0
	elif A <= 1.75e+73:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -7.2e+104)
		tmp = t_1;
	elseif (A <= -1.1e+85)
		tmp = t_0;
	elseif (A <= -2.1e-32)
		tmp = t_1;
	elseif (A <= -1.52e-176)
		tmp = t_0;
	elseif (A <= 9.8e-154)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 1.75e+73)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -7.2e+104)
		tmp = t_1;
	elseif (A <= -1.1e+85)
		tmp = t_0;
	elseif (A <= -2.1e-32)
		tmp = t_1;
	elseif (A <= -1.52e-176)
		tmp = t_0;
	elseif (A <= 9.8e-154)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 4000.0)
		tmp = t_0;
	elseif (A <= 1.75e+73)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = (180.0 / pi) * atan(((B - A) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7.2e+104], t$95$1, If[LessEqual[A, -1.1e+85], t$95$0, If[LessEqual[A, -2.1e-32], t$95$1, If[LessEqual[A, -1.52e-176], t$95$0, If[LessEqual[A, 9.8e-154], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4000.0], t$95$0, If[LessEqual[A, 1.75e+73], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -7.20000000000000001e104 or -1.1000000000000001e85 < A < -2.0999999999999999e-32

   1. Initial program 22.6%

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

      1. associate-*l/ 22.6%

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

      2. *-lft-identity 22.6%

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

      3. +-commutative 22.6%

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

      4. unpow2 22.6%

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

      5. unpow2 22.6%

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

      6. hypot-def 46.8%

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

   3. Simplified 46.8%

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

   4. Taylor expanded in A around -inf 72.3%

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

   if -7.20000000000000001e104 < A < -1.1000000000000001e85 or -2.0999999999999999e-32 < A < -1.52000000000000001e-176 or 9.79999999999999993e-154 < A < 4e3

   1. Initial program 60.9%

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

      1. associate-*l/ 60.9%

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

      2. *-lft-identity 60.9%

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

      3. +-commutative 60.9%

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

      4. unpow2 60.9%

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

      5. unpow2 60.9%

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

      6. hypot-def 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in A around 0 57.3%

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

      1. unpow2 57.3%

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

      2. unpow2 57.3%

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

      3. hypot-def 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in C around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

   if -1.52000000000000001e-176 < A < 9.79999999999999993e-154

   1. Initial program 56.9%

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

      1. associate-*l/ 56.9%

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

      2. *-lft-identity 56.9%

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

      3. +-commutative 56.9%

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

      4. unpow2 56.9%

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

      5. unpow2 56.9%

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

      6. hypot-def 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in B around -inf 56.4%

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

   5. Taylor expanded in A around 0 54.7%

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

   if 4e3 < A < 1.75000000000000001e73

   1. Initial program 29.2%

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

      1. associate-*r/ 29.2%

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

      2. unpow2 29.2%

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

   3. Simplified 29.2%

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

      1. associate--l- 29.2%

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

      2. +-commutative 29.2%

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

      3. unpow2 29.2%

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

      4. hypot-udef 74.2%

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

      5. flip-- 19.6%

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

      6. frac-times 18.3%

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

      7. *-un-lft-identity 18.3%

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

      8. pow2 18.3%

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

   5. Applied egg-rr 18.3%

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

      1. associate-+r+ 18.3%

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

   7. Simplified 18.3%

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

   8. Taylor expanded in A around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. mul-1-neg 59.9%

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

      3. +-commutative 59.9%

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

      4. unpow2 59.9%

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

      5. unpow2 59.9%

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

      6. hypot-def 90.0%

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

   10. Simplified 90.0%

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

       1. *-un-lft-identity 90.0%

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

       2. associate-/l* 85.8%

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

   12. Applied egg-rr 85.8%

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

       1. *-lft-identity 85.8%

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

       2. associate-/r/ 90.0%

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

   14. Simplified 90.0%

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

   15. Taylor expanded in B around 0 68.1%

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

   if 1.75000000000000001e73 < A

   1. Initial program 81.9%

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

      1. associate-*r/ 81.9%

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

      2. associate-*l/ 81.9%

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

      3. associate-*l/ 81.9%

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

      4. *-lft-identity 81.9%

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

      5. sub-neg 81.9%

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

      6. associate-+l- 81.9%

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

      7. sub-neg 81.9%

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

      8. remove-double-neg 81.9%

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

      9. +-commutative 81.9%

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

      10. unpow2 81.9%

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

      11. unpow2 81.9%

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

      12. hypot-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in B around -inf 84.3%

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

      1. neg-mul-1 84.3%

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

      2. unsub-neg 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in C around 0 82.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.52 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.8 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.75 \cdot 10^{+73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \]

Alternative 10: 57.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -4.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{180 \cdot t_1}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{t_1}{\pi}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1350:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -4.7e+104)
     (/ (* 180.0 t_1) PI)
     (if (<= A -1.1e+85)
       t_0
       (if (<= A -7.5e-29)
         (* 180.0 (/ t_1 PI))
         (if (<= A -1.6e-176)
           t_0
           (if (<= A 1e-153)
             (* 180.0 (/ (atan (/ (+ B C) B)) PI))
             (if (<= A 1350.0)
               t_0
               (if (<= A 3.1e+75)
                 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
                 (* (/ 180.0 PI) (atan (/ (- B A) B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -4.7e+104) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (A <= -1.1e+85) {
		tmp = t_0;
	} else if (A <= -7.5e-29) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (A <= -1.6e-176) {
		tmp = t_0;
	} else if (A <= 1e-153) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 1350.0) {
		tmp = t_0;
	} else if (A <= 3.1e+75) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -4.7e+104) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (A <= -1.1e+85) {
		tmp = t_0;
	} else if (A <= -7.5e-29) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (A <= -1.6e-176) {
		tmp = t_0;
	} else if (A <= 1e-153) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 1350.0) {
		tmp = t_0;
	} else if (A <= 3.1e+75) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -4.7e+104:
		tmp = (180.0 * t_1) / math.pi
	elif A <= -1.1e+85:
		tmp = t_0
	elif A <= -7.5e-29:
		tmp = 180.0 * (t_1 / math.pi)
	elif A <= -1.6e-176:
		tmp = t_0
	elif A <= 1e-153:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 1350.0:
		tmp = t_0
	elif A <= 3.1e+75:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -4.7e+104)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (A <= -1.1e+85)
		tmp = t_0;
	elseif (A <= -7.5e-29)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (A <= -1.6e-176)
		tmp = t_0;
	elseif (A <= 1e-153)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 1350.0)
		tmp = t_0;
	elseif (A <= 3.1e+75)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -4.7e+104)
		tmp = (180.0 * t_1) / pi;
	elseif (A <= -1.1e+85)
		tmp = t_0;
	elseif (A <= -7.5e-29)
		tmp = 180.0 * (t_1 / pi);
	elseif (A <= -1.6e-176)
		tmp = t_0;
	elseif (A <= 1e-153)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 1350.0)
		tmp = t_0;
	elseif (A <= 3.1e+75)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = (180.0 / pi) * atan(((B - A) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -4.7e+104], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.1e+85], t$95$0, If[LessEqual[A, -7.5e-29], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.6e-176], t$95$0, If[LessEqual[A, 1e-153], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1350.0], t$95$0, If[LessEqual[A, 3.1e+75], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -4.70000000000000017e104

   1. Initial program 11.4%

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

      1. associate-*r/ 11.4%

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

      2. unpow2 11.4%

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

   3. Simplified 11.4%

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

      1. associate--l- 11.1%

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

      2. +-commutative 11.1%

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

      3. unpow2 11.1%

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

      4. hypot-udef 24.7%

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

      5. flip-- 10.0%

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

      6. frac-times 5.2%

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

      7. *-un-lft-identity 5.2%

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

      8. pow2 5.2%

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

   5. Applied egg-rr 5.2%

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

      1. associate-+r+ 4.0%

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

   7. Simplified 4.0%

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

   8. Taylor expanded in A around -inf 78.7%

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

   if -4.70000000000000017e104 < A < -1.1000000000000001e85 or -7.50000000000000006e-29 < A < -1.59999999999999992e-176 or 1.00000000000000004e-153 < A < 1350

   1. Initial program 60.9%

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

      1. associate-*l/ 60.9%

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

      2. *-lft-identity 60.9%

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

      3. +-commutative 60.9%

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

      4. unpow2 60.9%

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

      5. unpow2 60.9%

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

      6. hypot-def 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in A around 0 57.3%

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

      1. unpow2 57.3%

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

      2. unpow2 57.3%

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

      3. hypot-def 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in C around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

   if -1.1000000000000001e85 < A < -7.50000000000000006e-29

   1. Initial program 39.8%

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

      1. associate-*l/ 39.8%

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

      2. *-lft-identity 39.8%

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

      3. +-commutative 39.8%

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

      4. unpow2 39.8%

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

      5. unpow2 39.8%

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

      6. hypot-def 50.6%

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

   3. Simplified 50.6%

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

   4. Taylor expanded in A around -inf 62.7%

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

   if -1.59999999999999992e-176 < A < 1.00000000000000004e-153

   1. Initial program 56.9%

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

      1. associate-*l/ 56.9%

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

      2. *-lft-identity 56.9%

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

      3. +-commutative 56.9%

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

      4. unpow2 56.9%

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

      5. unpow2 56.9%

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

      6. hypot-def 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in B around -inf 56.4%

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

   5. Taylor expanded in A around 0 54.7%

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

   if 1350 < A < 3.1000000000000001e75

   1. Initial program 29.2%

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

      1. associate-*r/ 29.2%

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

      2. unpow2 29.2%

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

   3. Simplified 29.2%

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

      1. associate--l- 29.2%

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

      2. +-commutative 29.2%

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

      3. unpow2 29.2%

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

      4. hypot-udef 74.2%

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

      5. flip-- 19.6%

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

      6. frac-times 18.3%

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

      7. *-un-lft-identity 18.3%

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

      8. pow2 18.3%

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

   5. Applied egg-rr 18.3%

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

      1. associate-+r+ 18.3%

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

   7. Simplified 18.3%

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

   8. Taylor expanded in A around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. mul-1-neg 59.9%

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

      3. +-commutative 59.9%

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

      4. unpow2 59.9%

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

      5. unpow2 59.9%

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

      6. hypot-def 90.0%

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

   10. Simplified 90.0%

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

       1. *-un-lft-identity 90.0%

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

       2. associate-/l* 85.8%

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

   12. Applied egg-rr 85.8%

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

       1. *-lft-identity 85.8%

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

       2. associate-/r/ 90.0%

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

   14. Simplified 90.0%

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

   15. Taylor expanded in B around 0 68.1%

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

   if 3.1000000000000001e75 < A

   1. Initial program 81.9%

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

      1. associate-*r/ 81.9%

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

      2. associate-*l/ 81.9%

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

      3. associate-*l/ 81.9%

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

      4. *-lft-identity 81.9%

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

      5. sub-neg 81.9%

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

      6. associate-+l- 81.9%

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

      7. sub-neg 81.9%

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

      8. remove-double-neg 81.9%

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

      9. +-commutative 81.9%

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

      10. unpow2 81.9%

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

      11. unpow2 81.9%

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

      12. hypot-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in B around -inf 84.3%

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

      1. neg-mul-1 84.3%

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

      2. unsub-neg 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in C around 0 82.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1350:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \end{array} \]

Alternative 11: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -1.9e-79)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -9.8e-169)
       t_0
       (if (<= B 1e-302)
         (* 180.0 (/ (atan (/ C B)) PI))
         (if (<= B 1.15e-187)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (if (<= B 2.1e-139)
             (* 180.0 (/ (atan (/ (- A) B)) PI))
             (if (<= B 2.05e-20) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (B <= -1.9e-79) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.8e-169) {
		tmp = t_0;
	} else if (B <= 1e-302) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 1.15e-187) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.1e-139) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 2.05e-20) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (B <= -1.9e-79) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.8e-169) {
		tmp = t_0;
	} else if (B <= 1e-302) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 1.15e-187) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.1e-139) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 2.05e-20) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if B <= -1.9e-79:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.8e-169:
		tmp = t_0
	elif B <= 1e-302:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 1.15e-187:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.1e-139:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 2.05e-20:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (B <= -1.9e-79)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.8e-169)
		tmp = t_0;
	elseif (B <= 1e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 1.15e-187)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.1e-139)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 2.05e-20)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (B <= -1.9e-79)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.8e-169)
		tmp = t_0;
	elseif (B <= 1e-302)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 1.15e-187)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.1e-139)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 2.05e-20)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.9e-79], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.8e-169], t$95$0, If[LessEqual[B, 1e-302], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-187], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-139], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.05e-20], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.9000000000000001e-79

   1. Initial program 54.7%

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

      1. associate-*l/ 54.7%

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

      2. *-lft-identity 54.7%

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

      3. +-commutative 54.7%

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

      4. unpow2 54.7%

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

      5. unpow2 54.7%

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

      6. hypot-def 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in B around -inf 51.7%

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

   if -1.9000000000000001e-79 < B < -9.7999999999999999e-169 or 2.10000000000000008e-139 < B < 2.05e-20

   1. Initial program 47.0%

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

      1. associate-*l/ 47.0%

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

      2. *-lft-identity 47.0%

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

      3. +-commutative 47.0%

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

      4. unpow2 47.0%

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

      5. unpow2 47.0%

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

      6. hypot-def 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in A around 0 29.3%

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

      1. unpow2 29.3%

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

      2. unpow2 29.3%

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

      3. hypot-def 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in C around inf 48.6%

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

   if -9.7999999999999999e-169 < B < 9.9999999999999996e-303

   1. Initial program 59.7%

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

      1. associate-*l/ 59.7%

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

      2. *-lft-identity 59.7%

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

      3. +-commutative 59.7%

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

      4. unpow2 59.7%

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

      5. unpow2 59.7%

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

      6. hypot-def 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in B around -inf 62.7%

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

   5. Taylor expanded in C around inf 44.1%

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

   if 9.9999999999999996e-303 < B < 1.14999999999999999e-187

   1. Initial program 40.5%

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

      1. associate-*l/ 40.5%

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

      2. *-lft-identity 40.5%

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

      3. +-commutative 40.5%

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

      4. unpow2 40.5%

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

      5. unpow2 40.5%

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

      6. hypot-def 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in C around inf 44.2%

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

      1. distribute-rgt1-in 44.2%

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

      2. metadata-eval 44.2%

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

      3. mul0-lft 44.2%

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

      4. metadata-eval 44.2%

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

   6. Simplified 44.2%

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

   if 1.14999999999999999e-187 < B < 2.10000000000000008e-139

   1. Initial program 90.0%

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

      1. associate-*l/ 90.0%

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

      2. *-lft-identity 90.0%

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

      3. +-commutative 90.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 90.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 90.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 90.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 78.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in A around inf 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 67.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   7. Simplified 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]

   if 2.05e-20 < B

   1. Initial program 54.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 66.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.8 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 45.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -1.35 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.36 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3800:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= A -1.35e-33)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -1.36e-176)
       t_0
       (if (<= A 3.2e-153)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= A 3800.0)
           t_0
           (if (<= A 7e+116)
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
             (* 180.0 (/ (atan (/ (- A) B)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (A <= -1.35e-33) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.36e-176) {
		tmp = t_0;
	} else if (A <= 3.2e-153) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3800.0) {
		tmp = t_0;
	} else if (A <= 7e+116) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (A <= -1.35e-33) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.36e-176) {
		tmp = t_0;
	} else if (A <= 3.2e-153) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3800.0) {
		tmp = t_0;
	} else if (A <= 7e+116) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if A <= -1.35e-33:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.36e-176:
		tmp = t_0
	elif A <= 3.2e-153:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3800.0:
		tmp = t_0
	elif A <= 7e+116:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (A <= -1.35e-33)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.36e-176)
		tmp = t_0;
	elseif (A <= 3.2e-153)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3800.0)
		tmp = t_0;
	elseif (A <= 7e+116)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (A <= -1.35e-33)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.36e-176)
		tmp = t_0;
	elseif (A <= 3.2e-153)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3800.0)
		tmp = t_0;
	elseif (A <= 7e+116)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan((-A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.35e-33], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.36e-176], t$95$0, If[LessEqual[A, 3.2e-153], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3800.0], t$95$0, If[LessEqual[A, 7e+116], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.35e-33

   1. Initial program 26.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 50.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 66.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -1.35e-33 < A < -1.36e-176 or 3.1999999999999999e-153 < A < 3800

   1. Initial program 60.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 46.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if -1.36e-176 < A < 3.1999999999999999e-153

   1. Initial program 56.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 88.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 41.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 3800 < A < 6.99999999999999993e116

   1. Initial program 40.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around 0 22.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around inf 57.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 6.99999999999999993e116 < A

   1. Initial program 87.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 96.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 89.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in A around inf 83.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. associate-*r/ 83.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 83.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   7. Simplified 83.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.36 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3800:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 45.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 450:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= A -1.12e-29)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -2.3e-176)
       t_0
       (if (<= A 4.4e-153)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= A 450.0)
           t_0
           (if (<= A 7e+116)
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
             (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (A <= -1.12e-29) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -2.3e-176) {
		tmp = t_0;
	} else if (A <= 4.4e-153) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 450.0) {
		tmp = t_0;
	} else if (A <= 7e+116) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (A <= -1.12e-29) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -2.3e-176) {
		tmp = t_0;
	} else if (A <= 4.4e-153) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 450.0) {
		tmp = t_0;
	} else if (A <= 7e+116) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if A <= -1.12e-29:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -2.3e-176:
		tmp = t_0
	elif A <= 4.4e-153:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 450.0:
		tmp = t_0
	elif A <= 7e+116:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (A <= -1.12e-29)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -2.3e-176)
		tmp = t_0;
	elseif (A <= 4.4e-153)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 450.0)
		tmp = t_0;
	elseif (A <= 7e+116)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (A <= -1.12e-29)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -2.3e-176)
		tmp = t_0;
	elseif (A <= 4.4e-153)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 450.0)
		tmp = t_0;
	elseif (A <= 7e+116)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.12e-29], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.3e-176], t$95$0, If[LessEqual[A, 4.4e-153], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 450.0], t$95$0, If[LessEqual[A, 7e+116], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.11999999999999995e-29

   1. Initial program 26.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 26.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 50.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 66.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -1.11999999999999995e-29 < A < -2.3000000000000001e-176 or 4.40000000000000001e-153 < A < 450

   1. Initial program 60.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 60.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 46.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if -2.3000000000000001e-176 < A < 4.40000000000000001e-153

   1. Initial program 56.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 56.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 88.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 41.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 450 < A < 6.99999999999999993e116

   1. Initial program 40.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around 0 22.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around inf 57.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 6.99999999999999993e116 < A

   1. Initial program 87.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 96.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around inf 84.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-2 \cdot A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]

   6. Simplified 84.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 450:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 52.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2700:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.3e-42)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 4e-130)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (if (<= A 2700.0)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 7e+116)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.3e-42) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 4e-130) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 2700.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 7e+116) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.3e-42) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 4e-130) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 2700.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 7e+116) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.3e-42:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 4e-130:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 2700.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 7e+116:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.3e-42)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 4e-130)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 2700.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 7e+116)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.3e-42)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 4e-130)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 2700.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 7e+116)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.3e-42], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4e-130], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2700.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7e+116], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -4.3000000000000001e-42

   1. Initial program 26.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 51.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 51.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 63.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -4.3000000000000001e-42 < A < 4.0000000000000003e-130

   1. Initial program 54.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 50.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in A around 0 49.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C + B}{B}\right)}}{\pi} \]

   if 4.0000000000000003e-130 < A < 2700

   1. Initial program 81.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 92.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 54.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 2700 < A < 6.99999999999999993e116

   1. Initial program 40.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around 0 22.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 22.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 64.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around inf 57.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 6.99999999999999993e116 < A

   1. Initial program 87.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 87.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 96.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around inf 84.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-2 \cdot A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]

   6. Simplified 84.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2700:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 54.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3800:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.8e-43)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 3e-130)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (if (<= A 3800.0)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 2.5e+72)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (* 180.0 (/ (atan (/ (- B A) B)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e-43) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 3e-130) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 3800.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 2.5e+72) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e-43) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 3e-130) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 3800.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 2.5e+72) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.8e-43:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 3e-130:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 3800.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 2.5e+72:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.8e-43)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 3e-130)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 3800.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 2.5e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.8e-43)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 3e-130)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 3800.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 2.5e+72)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.8e-43], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-130], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3800.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.5e+72], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -6.8000000000000001e-43

   1. Initial program 26.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 51.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 51.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 63.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -6.8000000000000001e-43 < A < 2.99999999999999986e-130

   1. Initial program 54.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 50.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in A around 0 49.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C + B}{B}\right)}}{\pi} \]

   if 2.99999999999999986e-130 < A < 3800

   1. Initial program 81.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 92.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 54.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 3800 < A < 2.49999999999999996e72

   1. Initial program 29.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 74.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around 0 23.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 23.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 23.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 68.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 68.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around inf 67.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   if 2.49999999999999996e72 < A

   1. Initial program 81.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 81.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 81.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 81.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 81.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 95.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 84.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in C around 0 82.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3800:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 45.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- A) B)) PI))))
   (if (<= B -4.8e-114)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1.6e-277)
       t_0
       (if (<= B 2.1e-184)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 3.4e+15) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-A / B)) / ((double) M_PI));
	double tmp;
	if (B <= -4.8e-114) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.6e-277) {
		tmp = t_0;
	} else if (B <= 2.1e-184) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.4e+15) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-A / B)) / Math.PI);
	double tmp;
	if (B <= -4.8e-114) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.6e-277) {
		tmp = t_0;
	} else if (B <= 2.1e-184) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.4e+15) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-A / B)) / math.pi)
	tmp = 0
	if B <= -4.8e-114:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.6e-277:
		tmp = t_0
	elif B <= 2.1e-184:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.4e+15:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi))
	tmp = 0.0
	if (B <= -4.8e-114)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.6e-277)
		tmp = t_0;
	elseif (B <= 2.1e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.4e+15)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-A / B)) / pi);
	tmp = 0.0;
	if (B <= -4.8e-114)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.6e-277)
		tmp = t_0;
	elseif (B <= 2.1e-184)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.4e+15)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.8e-114], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.6e-277], t$95$0, If[LessEqual[B, 2.1e-184], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.4e+15], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.8000000000000002e-114

   1. Initial program 52.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 52.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 52.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 52.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 52.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 75.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 49.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -4.8000000000000002e-114 < B < -1.5999999999999999e-277 or 2.0999999999999999e-184 < B < 3.4e15

   1. Initial program 60.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 60.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 60.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 60.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 60.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 76.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 55.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in A around inf 42.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. associate-*r/ 42.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 42.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   7. Simplified 42.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]

   if -1.5999999999999999e-277 < B < 2.0999999999999999e-184

   1. Initial program 43.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 43.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 43.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 43.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 43.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 43.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 82.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 43.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 43.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 43.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 43.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 43.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 43.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 3.4e15 < B

   1. Initial program 51.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 51.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 51.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 51.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 51.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 51.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 69.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-277}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 45.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-301}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -8.5e-189)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 1.5e-301)
       t_0
       (if (<= B 2.8e-196)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 4e-24) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -8.5e-189) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.5e-301) {
		tmp = t_0;
	} else if (B <= 2.8e-196) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 4e-24) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -8.5e-189) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.5e-301) {
		tmp = t_0;
	} else if (B <= 2.8e-196) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 4e-24) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -8.5e-189:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.5e-301:
		tmp = t_0
	elif B <= 2.8e-196:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 4e-24:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -8.5e-189)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.5e-301)
		tmp = t_0;
	elseif (B <= 2.8e-196)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 4e-24)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -8.5e-189)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.5e-301)
		tmp = t_0;
	elseif (B <= 2.8e-196)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 4e-24)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8.5e-189], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.5e-301], t$95$0, If[LessEqual[B, 2.8e-196], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-24], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.50000000000000068e-189

   1. Initial program 50.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 50.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 50.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 50.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 50.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 50.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 74.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 43.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -8.50000000000000068e-189 < B < 1.5e-301 or 2.7999999999999998e-196 < B < 3.99999999999999969e-24

   1. Initial program 64.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 64.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 64.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 64.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 64.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 60.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   5. Taylor expanded in C around inf 40.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   if 1.5e-301 < B < 2.7999999999999998e-196

   1. Initial program 38.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 38.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 38.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 38.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 38.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 38.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 76.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 42.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 42.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 42.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 42.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 42.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 42.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 3.99999999999999969e-24 < B

   1. Initial program 55.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 55.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 55.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 55.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 55.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 55.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18: 62.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.52 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.52e-23)
   (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))
   (* 180.0 (/ (atan (/ (- C B) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.52e-23) {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.52e-23) {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 2.52e-23:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 2.52e-23)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 2.52e-23)
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 2.52e-23], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 2.51999999999999992e-23

   1. Initial program 53.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 77.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 77.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 60.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   if 2.51999999999999992e-23 < B

   1. Initial program 54.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 80.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around 0 45.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 45.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 45.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 69.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 69.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - \mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around 0 68.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C + -1 \cdot B}}{B}\right)}{\pi} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C + \color{blue}{\left(-B\right)}}{B}\right)}{\pi} \]

      2. unsub-neg 68.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - B}}{B}\right)}{\pi} \]

   9. Simplified 68.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{C - B}}{B}\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2.52 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19: 66.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-264)
   (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))
   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-264) {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-264) {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-264:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-264)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-264)
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-264], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1e-264

   1. Initial program 53.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 77.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 77.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 66.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   if -1e-264 < B

   1. Initial program 54.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 66.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 66.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 66.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 66.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20: 66.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-264)
   (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-264) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-264) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-264:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-264)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-264)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-264], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1e-264

   1. Initial program 53.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 53.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 53.2%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 53.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 53.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 53.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 53.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 53.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 53.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 53.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 53.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 53.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 74.4%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 66.8%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 66.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 66.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 66.8%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   if -1e-264 < B

   1. Initial program 54.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 66.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 66.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 66.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 66.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 21: 44.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-133)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e-184)
     (* 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 <= -7.2e-133) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-184) {
		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 <= -7.2e-133) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-184) {
		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 <= -7.2e-133:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-184:
		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 <= -7.2e-133)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-184)
		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 <= -7.2e-133)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-184)
		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, -7.2e-133], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-184], 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 < -7.2000000000000008e-133

   1. Initial program 53.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 75.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 75.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 46.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -7.2000000000000008e-133 < B < 4.80000000000000049e-184

   1. Initial program 49.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 35.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 35.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 35.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 35.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 35.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 35.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 4.80000000000000049e-184 < B

   1. Initial program 56.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 56.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 56.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 56.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 56.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 78.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 51.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.35 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.35e-306)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.35e-306) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.35e-306) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.35e-306:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.35e-306)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.35e-306)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.35e-306], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -2.3500000000000001e-306

   1. Initial program 54.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 77.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 38.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -2.3500000000000001e-306 < B

   1. Initial program 53.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 78.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 43.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.35 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 23: 21.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.8%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Step-by-step derivation

   1. associate-*l/ 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

   2. *-lft-identity 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

   3. +-commutative 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

   4. unpow2 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

   5. unpow2 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

   6. hypot-def 78.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

3. Simplified 78.4%

   \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

4. Taylor expanded in B around inf 24.3%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

5. Final simplification 24.3%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023185 
(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)))