ABCF->ab-angle angle

Percentage Accurate: 53.6% → 87.9%

Time: 29.6s

Alternatives: 26

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-29} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -2e-29) (not (<= t_0 0.0)))
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -2e-29) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -2e-29) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -2e-29) or not (t_0 <= 0.0):
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -2e-29) || !(t_0 <= 0.0))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -2e-29) || ~((t_0 <= 0.0)))
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[t$95$0, -2e-29], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -1.99999999999999989e-29 or 0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 58.4%

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

      1. associate-*l/ 58.4%

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

      2. *-lft-identity 58.4%

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

      3. +-commutative 58.4%

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

      4. unpow2 58.4%

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

      5. unpow2 58.4%

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

      6. hypot-def 90.5%

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

   3. Simplified 90.5%

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

   if -1.99999999999999989e-29 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 23.5%

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

      1. associate-*r/ 23.5%

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

      2. unpow2 23.5%

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

   3. Simplified 23.5%

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

      1. *-commutative 23.5%

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

      2. associate--l- 13.2%

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

      3. +-commutative 13.2%

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

      4. unpow2 13.2%

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

      5. hypot-udef 13.2%

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

      6. div-inv 13.2%

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

      7. clear-num 13.2%

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

   5. Applied egg-rr 13.2%

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

   6. Taylor expanded in A around -inf 97.3%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -2 \cdot 10^{-29} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \end{array} \]

Alternative 2: 77.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.32 \cdot 10^{+36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.32e+36)
   (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI)
   (if (<= A 1.55e+60)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.32e+36) {
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	} else if (A <= 1.55e+60) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.32e+36) {
		tmp = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	} else if (A <= 1.55e+60) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.32e+36:
		tmp = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	elif A <= 1.55e+60:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.32e+36)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi);
	elseif (A <= 1.55e+60)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.32e+36)
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	elseif (A <= 1.55e+60)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.32e+36], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.55e+60], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.3200000000000001e36

   1. Initial program 18.3%

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

      1. associate-*r/ 18.3%

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

      2. unpow2 18.3%

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

   3. Simplified 18.3%

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

      1. *-commutative 18.3%

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

      2. associate--l- 11.8%

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

      3. +-commutative 11.8%

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

      4. unpow2 11.8%

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

      5. hypot-udef 36.0%

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

      6. div-inv 36.0%

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

      7. clear-num 36.0%

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

   5. Applied egg-rr 36.0%

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

   6. Taylor expanded in A around -inf 79.5%

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

   if -1.3200000000000001e36 < A < 1.55e60

   1. Initial program 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*l/ 58.2%

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

      3. associate-*l/ 58.2%

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

      4. *-lft-identity 58.2%

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

      5. sub-neg 58.2%

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

      6. associate-+l- 58.1%

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

      7. sub-neg 58.1%

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

      8. remove-double-neg 58.1%

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

      9. +-commutative 58.1%

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

      10. unpow2 58.1%

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

      11. unpow2 58.1%

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

      12. hypot-def 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in A around 0 56.4%

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

      1. unpow2 56.4%

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

      2. unpow2 56.4%

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

      3. hypot-def 81.0%

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

   6. Simplified 81.0%

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

   if 1.55e60 < A

   1. Initial program 77.5%

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

      1. associate-*l/ 77.5%

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

      2. *-lft-identity 77.5%

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

      3. +-commutative 77.5%

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

      4. unpow2 77.5%

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

      5. unpow2 77.5%

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

      6. hypot-def 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 77.5%

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

      1. mul-1-neg 77.5%

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

      2. +-commutative 77.5%

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

      3. unpow2 77.5%

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

      4. unpow2 77.5%

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

      5. hypot-def 92.4%

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

   6. Simplified 92.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.32 \cdot 10^{+36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 78.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.55 \cdot 10^{+42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.42e-67)
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot A B))) B)))
   (if (<= C 2.55e+42)
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI))
     (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.42e-67) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(A, B))) / B));
	} else if (C <= 2.55e+42) {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.42e-67) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(A, B))) / B));
	} else if (C <= 2.55e+42) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.42e-67:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(A, B))) / B))
	elif C <= 2.55e+42:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.42e-67)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(A, B))) / B)));
	elseif (C <= 2.55e+42)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.42e-67)
		tmp = (180.0 / pi) * atan(((C - (A + hypot(A, B))) / B));
	elseif (C <= 2.55e+42)
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	else
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.42e-67], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.55e+42], 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 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.42000000000000004e-67

   1. Initial program 77.4%

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

      1. associate-*r/ 77.4%

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

      2. associate-*l/ 77.4%

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

      3. associate-*l/ 77.4%

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

      4. *-lft-identity 77.4%

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

      5. sub-neg 77.4%

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

      6. associate-+l- 77.3%

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

      7. sub-neg 77.3%

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

      8. remove-double-neg 77.3%

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

      9. +-commutative 77.3%

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

      10. unpow2 77.3%

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

      11. unpow2 77.3%

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

      12. hypot-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in C around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. unpow2 76.9%

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

      3. unpow2 76.9%

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

      4. hypot-def 93.1%

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

   6. Simplified 93.1%

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

   if -1.42000000000000004e-67 < C < 2.55e42

   1. Initial program 57.0%

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

      1. associate-*l/ 57.0%

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

      2. *-lft-identity 57.0%

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

      3. +-commutative 57.0%

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

      4. unpow2 57.0%

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

      5. unpow2 57.0%

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

      6. hypot-def 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in C around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. +-commutative 54.9%

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

      3. unpow2 54.9%

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

      4. unpow2 54.9%

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

      5. hypot-def 81.2%

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

   6. Simplified 81.2%

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

   if 2.55e42 < C

   1. Initial program 18.9%

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

      1. associate-*r/ 18.9%

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

      2. unpow2 18.9%

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

   3. Simplified 18.9%

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

      1. *-commutative 18.9%

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

      2. associate--l- 16.9%

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

      3. +-commutative 16.9%

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

      4. unpow2 16.9%

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

      5. hypot-udef 57.6%

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

      6. div-inv 57.6%

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

      7. clear-num 57.6%

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

   5. Applied egg-rr 57.6%

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

   6. Taylor expanded in A around -inf 77.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.55 \cdot 10^{+42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \end{array} \]

Alternative 4: 76.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.6e+35)
   (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI)
   (if (<= A 3.9e+90)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+35) {
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	} else if (A <= 3.9e+90) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+35) {
		tmp = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	} else if (A <= 3.9e+90) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.6e+35:
		tmp = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	elif A <= 3.9e+90:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.6e+35)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi);
	elseif (A <= 3.9e+90)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.6e+35)
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	elseif (A <= 3.9e+90)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.6e+35], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.9e+90], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.6e35

   1. Initial program 18.3%

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

      1. associate-*r/ 18.3%

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

      2. unpow2 18.3%

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

   3. Simplified 18.3%

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

      1. *-commutative 18.3%

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

      2. associate--l- 11.8%

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

      3. +-commutative 11.8%

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

      4. unpow2 11.8%

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

      5. hypot-udef 36.0%

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

      6. div-inv 36.0%

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

      7. clear-num 36.0%

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

   5. Applied egg-rr 36.0%

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

   6. Taylor expanded in A around -inf 79.5%

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

   if -3.6e35 < A < 3.9000000000000002e90

   1. Initial program 57.7%

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

      1. associate-*r/ 57.7%

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

      2. associate-*l/ 57.7%

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

      3. associate-*l/ 57.7%

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

      4. *-lft-identity 57.7%

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

      5. sub-neg 57.7%

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

      6. associate-+l- 57.7%

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

      7. sub-neg 57.7%

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

      8. remove-double-neg 57.7%

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

      9. +-commutative 57.7%

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

      10. unpow2 57.7%

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

      11. unpow2 57.7%

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

      12. hypot-def 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in A around 0 55.6%

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

      1. unpow2 55.6%

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

      2. unpow2 55.6%

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

      3. hypot-def 81.5%

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

   6. Simplified 81.5%

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

   if 3.9000000000000002e90 < A

   1. Initial program 83.0%

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

      1. associate-*l/ 83.0%

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

      2. *-lft-identity 83.0%

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

      3. +-commutative 83.0%

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

      4. unpow2 83.0%

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

      5. unpow2 83.0%

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

      6. hypot-def 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 88.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 77.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e+36)
   (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI)
   (if (<= A 1.05e+58)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+36) {
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	} else if (A <= 1.05e+58) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+36) {
		tmp = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	} else if (A <= 1.05e+58) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+36:
		tmp = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	elif A <= 1.05e+58:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+36)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi);
	elseif (A <= 1.05e+58)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e+36)
		tmp = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	elseif (A <= 1.05e+58)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+36], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.05e+58], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.0999999999999999e36

   1. Initial program 18.3%

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

      1. associate-*r/ 18.3%

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

      2. unpow2 18.3%

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

   3. Simplified 18.3%

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

      1. *-commutative 18.3%

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

      2. associate--l- 11.8%

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

      3. +-commutative 11.8%

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

      4. unpow2 11.8%

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

      5. hypot-udef 36.0%

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

      6. div-inv 36.0%

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

      7. clear-num 36.0%

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

   5. Applied egg-rr 36.0%

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

   6. Taylor expanded in A around -inf 79.5%

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

   if -3.0999999999999999e36 < A < 1.05000000000000006e58

   1. Initial program 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*l/ 58.2%

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

      3. associate-*l/ 58.2%

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

      4. *-lft-identity 58.2%

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

      5. sub-neg 58.2%

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

      6. associate-+l- 58.1%

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

      7. sub-neg 58.1%

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

      8. remove-double-neg 58.1%

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

      9. +-commutative 58.1%

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

      10. unpow2 58.1%

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

      11. unpow2 58.1%

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

      12. hypot-def 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in A around 0 56.4%

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

      1. unpow2 56.4%

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

      2. unpow2 56.4%

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

      3. hypot-def 81.0%

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

   6. Simplified 81.0%

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

   if 1.05000000000000006e58 < A

   1. Initial program 77.5%

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

      1. associate-*r/ 77.5%

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

      2. unpow2 77.5%

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

   3. Simplified 77.5%

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

      1. *-commutative 77.5%

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

      2. associate--l- 77.5%

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

      3. +-commutative 77.5%

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

      4. unpow2 77.5%

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

      5. hypot-udef 99.9%

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

      6. div-inv 99.9%

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

      7. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in C around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. mul-1-neg 77.5%

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

      3. +-commutative 77.5%

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

      4. unpow2 77.5%

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

      5. unpow2 77.5%

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

      6. hypot-def 92.3%

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

   8. Simplified 92.3%

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

      1. expm1-log1p-u 52.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)\right)}}{\pi} \]

      2. expm1-udef 52.3%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)} - 1}}{\pi} \]

      3. distribute-frac-neg 52.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1}{\pi} \]

      4. atan-neg 52.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1}{\pi} \]

   10. Applied egg-rr 52.3%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1}}{\pi} \]
   11. Step-by-step derivation

       1. expm1-def 52.3%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 92.3%

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

       3. distribute-rgt-neg-out 92.3%

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

       4. distribute-lft-neg-in 92.3%

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

       5. metadata-eval 92.3%

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

   12. Simplified 92.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 60.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.2 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.4 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.38 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{A \cdot A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (/ (* 180.0 (atan (/ 1.0 (+ (/ (- A C) B) 1.0)))) PI)))
   (if (<= B -4.2e-124)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -1.65e-197)
       t_0
       (if (<= B -9.4e-237)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -7.4e-295)
           t_0
           (if (<= B 1.05e-307)
             t_1
             (if (<= B 1.38e-250)
               t_2
               (if (<= B 1e-187)
                 t_1
                 (if (<= B 3.8e-169)
                   t_2
                   (if (<= B 6.5e-105)
                     (*
                      180.0
                      (/ (atan (* 0.5 (+ (/ B A) (/ (* B C) (* A A))))) PI))
                     (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / ((double) M_PI);
	double tmp;
	if (B <= -4.2e-124) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -1.65e-197) {
		tmp = t_0;
	} else if (B <= -9.4e-237) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -7.4e-295) {
		tmp = t_0;
	} else if (B <= 1.05e-307) {
		tmp = t_1;
	} else if (B <= 1.38e-250) {
		tmp = t_2;
	} else if (B <= 1e-187) {
		tmp = t_1;
	} else if (B <= 3.8e-169) {
		tmp = t_2;
	} else if (B <= 6.5e-105) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B * C) / (A * A))))) / ((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 t_0 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = (180.0 * Math.atan((1.0 / (((A - C) / B) + 1.0)))) / Math.PI;
	double tmp;
	if (B <= -4.2e-124) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -1.65e-197) {
		tmp = t_0;
	} else if (B <= -9.4e-237) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -7.4e-295) {
		tmp = t_0;
	} else if (B <= 1.05e-307) {
		tmp = t_1;
	} else if (B <= 1.38e-250) {
		tmp = t_2;
	} else if (B <= 1e-187) {
		tmp = t_1;
	} else if (B <= 3.8e-169) {
		tmp = t_2;
	} else if (B <= 6.5e-105) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B * C) / (A * A))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = (180.0 * math.atan((1.0 / (((A - C) / B) + 1.0)))) / math.pi
	tmp = 0
	if B <= -4.2e-124:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -1.65e-197:
		tmp = t_0
	elif B <= -9.4e-237:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -7.4e-295:
		tmp = t_0
	elif B <= 1.05e-307:
		tmp = t_1
	elif B <= 1.38e-250:
		tmp = t_2
	elif B <= 1e-187:
		tmp = t_1
	elif B <= 3.8e-169:
		tmp = t_2
	elif B <= 6.5e-105:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B * C) / (A * A))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(Float64(A - C) / B) + 1.0)))) / pi)
	tmp = 0.0
	if (B <= -4.2e-124)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -1.65e-197)
		tmp = t_0;
	elseif (B <= -9.4e-237)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -7.4e-295)
		tmp = t_0;
	elseif (B <= 1.05e-307)
		tmp = t_1;
	elseif (B <= 1.38e-250)
		tmp = t_2;
	elseif (B <= 1e-187)
		tmp = t_1;
	elseif (B <= 3.8e-169)
		tmp = t_2;
	elseif (B <= 6.5e-105)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B * C) / Float64(A * A))))) / 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)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / pi;
	tmp = 0.0;
	if (B <= -4.2e-124)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -1.65e-197)
		tmp = t_0;
	elseif (B <= -9.4e-237)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -7.4e-295)
		tmp = t_0;
	elseif (B <= 1.05e-307)
		tmp = t_1;
	elseif (B <= 1.38e-250)
		tmp = t_2;
	elseif (B <= 1e-187)
		tmp = t_1;
	elseif (B <= 3.8e-169)
		tmp = t_2;
	elseif (B <= 6.5e-105)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B * C) / (A * A))))) / pi);
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -4.2e-124], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.65e-197], t$95$0, If[LessEqual[B, -9.4e-237], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.4e-295], t$95$0, If[LessEqual[B, 1.05e-307], t$95$1, If[LessEqual[B, 1.38e-250], t$95$2, If[LessEqual[B, 1e-187], t$95$1, If[LessEqual[B, 3.8e-169], t$95$2, If[LessEqual[B, 6.5e-105], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B * C), $MachinePrecision] / N[(A * A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 7 regimes

2. if B < -4.2000000000000002e-124

   1. Initial program 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.7%

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

      3. associate-*l/ 56.7%

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

      4. *-lft-identity 56.7%

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

      5. sub-neg 56.7%

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

      6. associate-+l- 56.6%

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

      7. sub-neg 56.6%

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

      8. remove-double-neg 56.6%

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

      9. +-commutative 56.6%

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

      10. unpow2 56.6%

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

      11. unpow2 56.6%

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

      12. hypot-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in B around -inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. unsub-neg 77.2%

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

   6. Simplified 77.2%

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

   if -4.2000000000000002e-124 < B < -1.6499999999999999e-197 or -9.3999999999999996e-237 < B < -7.3999999999999999e-295

   1. Initial program 29.3%

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

      1. associate-*r/ 29.3%

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

      2. unpow2 29.3%

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

   3. Simplified 29.3%

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

      1. *-commutative 29.3%

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

      2. associate--l- 28.2%

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

      3. +-commutative 28.2%

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

      4. unpow2 28.2%

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

      5. hypot-udef 59.8%

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

      6. div-inv 59.8%

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

      7. clear-num 59.8%

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

   5. Applied egg-rr 59.8%

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

   6. Taylor expanded in A around 0 25.7%

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

      1. unpow2 25.7%

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

      2. unpow2 25.7%

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

      3. hypot-def 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in C around inf 66.1%

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

       1. *-un-lft-identity 66.1%

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

       2. associate-/l* 66.4%

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

   11. Applied egg-rr 66.4%

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

   if -1.6499999999999999e-197 < B < -9.3999999999999996e-237

   1. Initial program 72.5%

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

      1. associate-*l/ 72.5%

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

      2. *-lft-identity 72.5%

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

      3. +-commutative 72.5%

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

      4. unpow2 72.5%

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

      5. unpow2 72.5%

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

      6. hypot-def 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in A around -inf 72.2%

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

   if -7.3999999999999999e-295 < B < 1.0500000000000001e-307 or 1.38e-250 < B < 1e-187

   1. Initial program 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*l/ 80.8%

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

      4. *-lft-identity 80.8%

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

      5. sub-neg 80.8%

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

      6. associate-+l- 80.7%

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

      7. sub-neg 80.7%

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

      8. remove-double-neg 80.7%

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

      9. +-commutative 80.7%

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

      10. unpow2 80.7%

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

      11. unpow2 80.7%

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

      12. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. neg-mul-1 80.6%

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

      2. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in C around inf 80.7%

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

   if 1.0500000000000001e-307 < B < 1.38e-250 or 1e-187 < B < 3.8e-169

   1. Initial program 40.2%

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

      1. associate-*r/ 40.2%

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

      2. unpow2 40.2%

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

   3. Simplified 40.2%

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

      1. *-commutative 40.2%

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

      2. associate--l- 33.5%

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

      3. +-commutative 33.5%

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

      4. unpow2 33.5%

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

      5. hypot-udef 63.8%

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

      6. div-inv 63.8%

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

      7. clear-num 63.8%

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

   5. Applied egg-rr 63.8%

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

   6. Taylor expanded in B around -inf 66.6%

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

      1. associate-*r/ 66.6%

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

      2. neg-mul-1 66.6%

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

      3. sub-neg 66.6%

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

      4. +-commutative 66.6%

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

      5. distribute-neg-in 66.6%

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

      6. remove-double-neg 66.6%

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

      7. sub-neg 66.6%

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

   8. Simplified 66.6%

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

   if 3.8e-169 < B < 6.50000000000000006e-105

   1. Initial program 33.5%

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

      1. associate-*l/ 33.5%

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

      2. *-lft-identity 33.5%

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

      3. +-commutative 33.5%

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

      4. unpow2 33.5%

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

      5. unpow2 33.5%

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

      6. hypot-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in A around -inf 67.5%

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

      1. distribute-lft-out 67.5%

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

      2. *-commutative 67.5%

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

      3. unpow2 67.5%

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

   6. Simplified 67.5%

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

   if 6.50000000000000006e-105 < B

   1. Initial program 57.4%

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

      1. associate-*l/ 57.4%

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

      2. *-lft-identity 57.4%

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

      3. +-commutative 57.4%

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

      4. unpow2 57.4%

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

      5. unpow2 57.4%

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

      6. hypot-def 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in B around inf 80.1%

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

      1. neg-mul-1 80.1%

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

      2. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -9.4 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.38 \cdot 10^{-250}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B \cdot C}{A \cdot A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 60.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.8 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.75 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (/ (* 180.0 (atan (/ 1.0 (+ (/ (- A C) B) 1.0)))) PI)))
   (if (<= B -3.8e-124)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -6e-192)
       t_0
       (if (<= B -3.4e-235)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -3.75e-295)
           t_0
           (if (<= B 1.4e-307)
             t_1
             (if (<= B 5.5e-251)
               t_2
               (if (<= B 1.25e-187)
                 t_1
                 (if (<= B 4.5e-171)
                   t_2
                   (if (<= B 9e-106)
                     (/
                      (* 180.0 (atan (* 0.5 (* (/ B A) (+ (/ C A) 1.0)))))
                      PI)
                     (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / ((double) M_PI);
	double tmp;
	if (B <= -3.8e-124) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -6e-192) {
		tmp = t_0;
	} else if (B <= -3.4e-235) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -3.75e-295) {
		tmp = t_0;
	} else if (B <= 1.4e-307) {
		tmp = t_1;
	} else if (B <= 5.5e-251) {
		tmp = t_2;
	} else if (B <= 1.25e-187) {
		tmp = t_1;
	} else if (B <= 4.5e-171) {
		tmp = t_2;
	} else if (B <= 9e-106) {
		tmp = (180.0 * atan((0.5 * ((B / A) * ((C / A) + 1.0))))) / ((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 t_0 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = (180.0 * Math.atan((1.0 / (((A - C) / B) + 1.0)))) / Math.PI;
	double tmp;
	if (B <= -3.8e-124) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -6e-192) {
		tmp = t_0;
	} else if (B <= -3.4e-235) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -3.75e-295) {
		tmp = t_0;
	} else if (B <= 1.4e-307) {
		tmp = t_1;
	} else if (B <= 5.5e-251) {
		tmp = t_2;
	} else if (B <= 1.25e-187) {
		tmp = t_1;
	} else if (B <= 4.5e-171) {
		tmp = t_2;
	} else if (B <= 9e-106) {
		tmp = (180.0 * Math.atan((0.5 * ((B / A) * ((C / A) + 1.0))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = (180.0 * math.atan((1.0 / (((A - C) / B) + 1.0)))) / math.pi
	tmp = 0
	if B <= -3.8e-124:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -6e-192:
		tmp = t_0
	elif B <= -3.4e-235:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -3.75e-295:
		tmp = t_0
	elif B <= 1.4e-307:
		tmp = t_1
	elif B <= 5.5e-251:
		tmp = t_2
	elif B <= 1.25e-187:
		tmp = t_1
	elif B <= 4.5e-171:
		tmp = t_2
	elif B <= 9e-106:
		tmp = (180.0 * math.atan((0.5 * ((B / A) * ((C / A) + 1.0))))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(Float64(A - C) / B) + 1.0)))) / pi)
	tmp = 0.0
	if (B <= -3.8e-124)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -6e-192)
		tmp = t_0;
	elseif (B <= -3.4e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -3.75e-295)
		tmp = t_0;
	elseif (B <= 1.4e-307)
		tmp = t_1;
	elseif (B <= 5.5e-251)
		tmp = t_2;
	elseif (B <= 1.25e-187)
		tmp = t_1;
	elseif (B <= 4.5e-171)
		tmp = t_2;
	elseif (B <= 9e-106)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(Float64(B / A) * Float64(Float64(C / A) + 1.0))))) / 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)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / pi;
	tmp = 0.0;
	if (B <= -3.8e-124)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -6e-192)
		tmp = t_0;
	elseif (B <= -3.4e-235)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -3.75e-295)
		tmp = t_0;
	elseif (B <= 1.4e-307)
		tmp = t_1;
	elseif (B <= 5.5e-251)
		tmp = t_2;
	elseif (B <= 1.25e-187)
		tmp = t_1;
	elseif (B <= 4.5e-171)
		tmp = t_2;
	elseif (B <= 9e-106)
		tmp = (180.0 * atan((0.5 * ((B / A) * ((C / A) + 1.0))))) / pi;
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -3.8e-124], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6e-192], t$95$0, If[LessEqual[B, -3.4e-235], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.75e-295], t$95$0, If[LessEqual[B, 1.4e-307], t$95$1, If[LessEqual[B, 5.5e-251], t$95$2, If[LessEqual[B, 1.25e-187], t$95$1, If[LessEqual[B, 4.5e-171], t$95$2, If[LessEqual[B, 9e-106], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] * N[(N[(C / A), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 7 regimes

2. if B < -3.80000000000000012e-124

   1. Initial program 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.7%

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

      3. associate-*l/ 56.7%

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

      4. *-lft-identity 56.7%

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

      5. sub-neg 56.7%

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

      6. associate-+l- 56.6%

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

      7. sub-neg 56.6%

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

      8. remove-double-neg 56.6%

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

      9. +-commutative 56.6%

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

      10. unpow2 56.6%

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

      11. unpow2 56.6%

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

      12. hypot-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in B around -inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. unsub-neg 77.2%

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

   6. Simplified 77.2%

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

   if -3.80000000000000012e-124 < B < -5.9999999999999998e-192 or -3.39999999999999972e-235 < B < -3.7499999999999998e-295

   1. Initial program 29.3%

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

      1. associate-*r/ 29.3%

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

      2. unpow2 29.3%

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

   3. Simplified 29.3%

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

      1. *-commutative 29.3%

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

      2. associate--l- 28.2%

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

      3. +-commutative 28.2%

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

      4. unpow2 28.2%

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

      5. hypot-udef 59.8%

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

      6. div-inv 59.8%

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

      7. clear-num 59.8%

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

   5. Applied egg-rr 59.8%

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

   6. Taylor expanded in A around 0 25.7%

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

      1. unpow2 25.7%

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

      2. unpow2 25.7%

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

      3. hypot-def 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in C around inf 66.1%

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

       1. *-un-lft-identity 66.1%

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

       2. associate-/l* 66.4%

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

   11. Applied egg-rr 66.4%

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

   if -5.9999999999999998e-192 < B < -3.39999999999999972e-235

   1. Initial program 72.5%

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

      1. associate-*l/ 72.5%

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

      2. *-lft-identity 72.5%

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

      3. +-commutative 72.5%

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

      4. unpow2 72.5%

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

      5. unpow2 72.5%

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

      6. hypot-def 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in A around -inf 72.2%

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

   if -3.7499999999999998e-295 < B < 1.4e-307 or 5.5e-251 < B < 1.2499999999999999e-187

   1. Initial program 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*l/ 80.8%

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

      4. *-lft-identity 80.8%

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

      5. sub-neg 80.8%

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

      6. associate-+l- 80.7%

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

      7. sub-neg 80.7%

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

      8. remove-double-neg 80.7%

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

      9. +-commutative 80.7%

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

      10. unpow2 80.7%

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

      11. unpow2 80.7%

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

      12. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. neg-mul-1 80.6%

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

      2. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in C around inf 80.7%

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

   if 1.4e-307 < B < 5.5e-251 or 1.2499999999999999e-187 < B < 4.5000000000000004e-171

   1. Initial program 40.2%

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

      1. associate-*r/ 40.2%

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

      2. unpow2 40.2%

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

   3. Simplified 40.2%

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

      1. *-commutative 40.2%

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

      2. associate--l- 33.5%

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

      3. +-commutative 33.5%

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

      4. unpow2 33.5%

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

      5. hypot-udef 63.8%

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

      6. div-inv 63.8%

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

      7. clear-num 63.8%

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

   5. Applied egg-rr 63.8%

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

   6. Taylor expanded in B around -inf 66.6%

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

      1. associate-*r/ 66.6%

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

      2. neg-mul-1 66.6%

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

      3. sub-neg 66.6%

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

      4. +-commutative 66.6%

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

      5. distribute-neg-in 66.6%

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

      6. remove-double-neg 66.6%

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

      7. sub-neg 66.6%

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

   8. Simplified 66.6%

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

   if 4.5000000000000004e-171 < B < 8.99999999999999911e-106

   1. Initial program 33.5%

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

      1. associate-*r/ 33.5%

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

      2. unpow2 33.5%

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

   3. Simplified 33.5%

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

      1. *-commutative 33.5%

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

      2. associate--l- 33.9%

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

      3. +-commutative 33.9%

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

      4. unpow2 33.9%

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

      5. hypot-udef 55.6%

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

      6. div-inv 55.6%

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

      7. clear-num 55.6%

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

   5. Applied egg-rr 55.6%

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

   6. Taylor expanded in A around -inf 67.4%

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

      1. distribute-lft-in 67.4%

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

      2. *-commutative 67.4%

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

      3. unpow2 67.4%

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

      4. times-frac 67.4%

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

      5. *-rgt-identity 67.4%

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

      6. distribute-lft-out 67.4%

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

   8. Simplified 67.4%

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

   if 8.99999999999999911e-106 < B

   1. Initial program 57.4%

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

      1. associate-*l/ 57.4%

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

      2. *-lft-identity 57.4%

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

      3. +-commutative 57.4%

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

      4. unpow2 57.4%

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

      5. unpow2 57.4%

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

      6. hypot-def 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in B around inf 80.1%

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

      1. neg-mul-1 80.1%

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

      2. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-192}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.75 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} \cdot \left(\frac{C}{A} + 1\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 59.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -7.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(C + -0.5 \cdot \frac{B \cdot B}{A}\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -7.6e-125)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -6.4e-189)
       t_0
       (if (<= B -4.5e-239)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -2.4e-296)
           t_0
           (if (<= B 1.55e-307)
             t_1
             (if (<= B 3.8e-251)
               (/ (* 180.0 (atan (/ 1.0 (+ (/ (- A C) B) 1.0)))) PI)
               (if (<= B 6e-187)
                 t_1
                 (if (<= B 4.8e-106)
                   (*
                    (/ 180.0 PI)
                    (atan (/ (- C (+ C (* -0.5 (/ (* B B) A)))) B)))
                   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -7.6e-125) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -6.4e-189) {
		tmp = t_0;
	} else if (B <= -4.5e-239) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -2.4e-296) {
		tmp = t_0;
	} else if (B <= 1.55e-307) {
		tmp = t_1;
	} else if (B <= 3.8e-251) {
		tmp = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / ((double) M_PI);
	} else if (B <= 6e-187) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (C + (-0.5 * ((B * 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 t_0 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -7.6e-125) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -6.4e-189) {
		tmp = t_0;
	} else if (B <= -4.5e-239) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -2.4e-296) {
		tmp = t_0;
	} else if (B <= 1.55e-307) {
		tmp = t_1;
	} else if (B <= 3.8e-251) {
		tmp = (180.0 * Math.atan((1.0 / (((A - C) / B) + 1.0)))) / Math.PI;
	} else if (B <= 6e-187) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (C + (-0.5 * ((B * B) / A)))) / B));
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -7.6e-125:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -6.4e-189:
		tmp = t_0
	elif B <= -4.5e-239:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -2.4e-296:
		tmp = t_0
	elif B <= 1.55e-307:
		tmp = t_1
	elif B <= 3.8e-251:
		tmp = (180.0 * math.atan((1.0 / (((A - C) / B) + 1.0)))) / math.pi
	elif B <= 6e-187:
		tmp = t_1
	elif B <= 4.8e-106:
		tmp = (180.0 / math.pi) * math.atan(((C - (C + (-0.5 * ((B * B) / A)))) / B))
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -7.6e-125)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -6.4e-189)
		tmp = t_0;
	elseif (B <= -4.5e-239)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -2.4e-296)
		tmp = t_0;
	elseif (B <= 1.55e-307)
		tmp = t_1;
	elseif (B <= 3.8e-251)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(Float64(A - C) / B) + 1.0)))) / pi);
	elseif (B <= 6e-187)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(C + Float64(-0.5 * Float64(Float64(B * 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)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -7.6e-125)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -6.4e-189)
		tmp = t_0;
	elseif (B <= -4.5e-239)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -2.4e-296)
		tmp = t_0;
	elseif (B <= 1.55e-307)
		tmp = t_1;
	elseif (B <= 3.8e-251)
		tmp = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / pi;
	elseif (B <= 6e-187)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = (180.0 / pi) * atan(((C - (C + (-0.5 * ((B * B) / A)))) / B));
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7.6e-125], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.4e-189], t$95$0, If[LessEqual[B, -4.5e-239], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.4e-296], t$95$0, If[LessEqual[B, 1.55e-307], t$95$1, If[LessEqual[B, 3.8e-251], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 6e-187], t$95$1, If[LessEqual[B, 4.8e-106], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(C + N[(-0.5 * N[(N[(B * B), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $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 7 regimes

2. if B < -7.6000000000000002e-125

   1. Initial program 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.7%

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

      3. associate-*l/ 56.7%

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

      4. *-lft-identity 56.7%

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

      5. sub-neg 56.7%

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

      6. associate-+l- 56.6%

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

      7. sub-neg 56.6%

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

      8. remove-double-neg 56.6%

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

      9. +-commutative 56.6%

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

      10. unpow2 56.6%

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

      11. unpow2 56.6%

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

      12. hypot-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in B around -inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. unsub-neg 77.2%

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

   6. Simplified 77.2%

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

   if -7.6000000000000002e-125 < B < -6.4000000000000001e-189 or -4.50000000000000013e-239 < B < -2.39999999999999996e-296

   1. Initial program 29.3%

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

      1. associate-*r/ 29.3%

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

      2. unpow2 29.3%

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

   3. Simplified 29.3%

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

      1. *-commutative 29.3%

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

      2. associate--l- 28.2%

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

      3. +-commutative 28.2%

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

      4. unpow2 28.2%

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

      5. hypot-udef 59.8%

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

      6. div-inv 59.8%

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

      7. clear-num 59.8%

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

   5. Applied egg-rr 59.8%

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

   6. Taylor expanded in A around 0 25.7%

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

      1. unpow2 25.7%

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

      2. unpow2 25.7%

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

      3. hypot-def 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in C around inf 66.1%

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

       1. *-un-lft-identity 66.1%

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

       2. associate-/l* 66.4%

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

   11. Applied egg-rr 66.4%

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

   if -6.4000000000000001e-189 < B < -4.50000000000000013e-239

   1. Initial program 72.5%

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

      1. associate-*l/ 72.5%

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

      2. *-lft-identity 72.5%

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

      3. +-commutative 72.5%

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

      4. unpow2 72.5%

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

      5. unpow2 72.5%

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

      6. hypot-def 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in A around -inf 72.2%

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

   if -2.39999999999999996e-296 < B < 1.5499999999999999e-307 or 3.7999999999999997e-251 < B < 6.00000000000000008e-187

   1. Initial program 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*l/ 80.8%

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

      4. *-lft-identity 80.8%

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

      5. sub-neg 80.8%

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

      6. associate-+l- 80.7%

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

      7. sub-neg 80.7%

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

      8. remove-double-neg 80.7%

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

      9. +-commutative 80.7%

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

      10. unpow2 80.7%

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

      11. unpow2 80.7%

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

      12. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. neg-mul-1 80.6%

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

      2. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in C around inf 80.7%

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

   if 1.5499999999999999e-307 < B < 3.7999999999999997e-251

   1. Initial program 48.1%

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

      1. associate-*r/ 48.1%

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

      2. unpow2 48.1%

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

   3. Simplified 48.1%

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

      1. *-commutative 48.1%

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

      2. associate--l- 38.3%

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

      3. +-commutative 38.3%

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

      4. unpow2 38.3%

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

      5. hypot-udef 73.5%

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

      6. div-inv 73.5%

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

      7. clear-num 73.5%

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

   5. Applied egg-rr 73.5%

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

   6. Taylor expanded in B around -inf 67.6%

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

      1. associate-*r/ 67.6%

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

      2. neg-mul-1 67.6%

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

      3. sub-neg 67.6%

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

      4. +-commutative 67.6%

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

      5. distribute-neg-in 67.6%

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

      6. remove-double-neg 67.6%

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

      7. sub-neg 67.6%

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

   8. Simplified 67.6%

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

   if 6.00000000000000008e-187 < B < 4.7999999999999995e-106

   1. Initial program 29.7%

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

      1. associate-*r/ 29.7%

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

      2. associate-*l/ 29.7%

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

      3. associate-*l/ 29.7%

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

      4. *-lft-identity 29.7%

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

      5. sub-neg 29.7%

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

      6. associate-+l- 30.0%

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

      7. sub-neg 30.0%

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

      8. remove-double-neg 30.0%

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

      9. +-commutative 30.0%

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

      10. unpow2 30.0%

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

      11. unpow2 30.0%

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

      12. hypot-def 50.8%

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

   3. Simplified 50.8%

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

   4. Taylor expanded in A around -inf 65.4%

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

      1. unpow2 65.4%

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

   6. Simplified 65.4%

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

   if 4.7999999999999995e-106 < B

   1. Initial program 57.4%

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

      1. associate-*l/ 57.4%

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

      2. *-lft-identity 57.4%

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

      3. +-commutative 57.4%

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

      4. unpow2 57.4%

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

      5. unpow2 57.4%

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

      6. hypot-def 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in B around inf 80.1%

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

      1. neg-mul-1 80.1%

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

      2. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(C + -0.5 \cdot \frac{B \cdot B}{A}\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 59.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := \frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-294}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (/ (* 180.0 (atan (/ 1.0 (+ (/ (- A C) B) 1.0)))) PI)))
   (if (<= B -1.3e-123)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -1.65e-187)
       t_0
       (if (<= B -5.1e-231)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -1.55e-294)
           t_0
           (if (<= B 2.1e-307)
             t_1
             (if (<= B 5.2e-252)
               t_2
               (if (<= B 3e-189)
                 t_1
                 (if (<= B 9e-104)
                   t_2
                   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / ((double) M_PI);
	double tmp;
	if (B <= -1.3e-123) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -1.65e-187) {
		tmp = t_0;
	} else if (B <= -5.1e-231) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -1.55e-294) {
		tmp = t_0;
	} else if (B <= 2.1e-307) {
		tmp = t_1;
	} else if (B <= 5.2e-252) {
		tmp = t_2;
	} else if (B <= 3e-189) {
		tmp = t_1;
	} else if (B <= 9e-104) {
		tmp = t_2;
	} 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 t_0 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = (180.0 * Math.atan((1.0 / (((A - C) / B) + 1.0)))) / Math.PI;
	double tmp;
	if (B <= -1.3e-123) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -1.65e-187) {
		tmp = t_0;
	} else if (B <= -5.1e-231) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -1.55e-294) {
		tmp = t_0;
	} else if (B <= 2.1e-307) {
		tmp = t_1;
	} else if (B <= 5.2e-252) {
		tmp = t_2;
	} else if (B <= 3e-189) {
		tmp = t_1;
	} else if (B <= 9e-104) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = (180.0 * math.atan((1.0 / (((A - C) / B) + 1.0)))) / math.pi
	tmp = 0
	if B <= -1.3e-123:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -1.65e-187:
		tmp = t_0
	elif B <= -5.1e-231:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -1.55e-294:
		tmp = t_0
	elif B <= 2.1e-307:
		tmp = t_1
	elif B <= 5.2e-252:
		tmp = t_2
	elif B <= 3e-189:
		tmp = t_1
	elif B <= 9e-104:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(Float64(A - C) / B) + 1.0)))) / pi)
	tmp = 0.0
	if (B <= -1.3e-123)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -1.65e-187)
		tmp = t_0;
	elseif (B <= -5.1e-231)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -1.55e-294)
		tmp = t_0;
	elseif (B <= 2.1e-307)
		tmp = t_1;
	elseif (B <= 5.2e-252)
		tmp = t_2;
	elseif (B <= 3e-189)
		tmp = t_1;
	elseif (B <= 9e-104)
		tmp = t_2;
	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)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = (180.0 * atan((1.0 / (((A - C) / B) + 1.0)))) / pi;
	tmp = 0.0;
	if (B <= -1.3e-123)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -1.65e-187)
		tmp = t_0;
	elseif (B <= -5.1e-231)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -1.55e-294)
		tmp = t_0;
	elseif (B <= 2.1e-307)
		tmp = t_1;
	elseif (B <= 5.2e-252)
		tmp = t_2;
	elseif (B <= 3e-189)
		tmp = t_1;
	elseif (B <= 9e-104)
		tmp = t_2;
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -1.3e-123], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.65e-187], t$95$0, If[LessEqual[B, -5.1e-231], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.55e-294], t$95$0, If[LessEqual[B, 2.1e-307], t$95$1, If[LessEqual[B, 5.2e-252], t$95$2, If[LessEqual[B, 3e-189], t$95$1, If[LessEqual[B, 9e-104], t$95$2, 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 6 regimes

2. if B < -1.29999999999999998e-123

   1. Initial program 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.7%

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

      3. associate-*l/ 56.7%

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

      4. *-lft-identity 56.7%

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

      5. sub-neg 56.7%

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

      6. associate-+l- 56.6%

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

      7. sub-neg 56.6%

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

      8. remove-double-neg 56.6%

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

      9. +-commutative 56.6%

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

      10. unpow2 56.6%

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

      11. unpow2 56.6%

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

      12. hypot-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in B around -inf 77.2%

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

      1. neg-mul-1 77.2%

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

      2. unsub-neg 77.2%

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

   6. Simplified 77.2%

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

   if -1.29999999999999998e-123 < B < -1.65e-187 or -5.1e-231 < B < -1.55000000000000002e-294

   1. Initial program 29.3%

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

      1. associate-*r/ 29.3%

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

      2. unpow2 29.3%

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

   3. Simplified 29.3%

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

      1. *-commutative 29.3%

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

      2. associate--l- 28.2%

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

      3. +-commutative 28.2%

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

      4. unpow2 28.2%

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

      5. hypot-udef 59.8%

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

      6. div-inv 59.8%

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

      7. clear-num 59.8%

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

   5. Applied egg-rr 59.8%

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

   6. Taylor expanded in A around 0 25.7%

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

      1. unpow2 25.7%

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

      2. unpow2 25.7%

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

      3. hypot-def 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in C around inf 66.1%

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

       1. *-un-lft-identity 66.1%

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

       2. associate-/l* 66.4%

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

   11. Applied egg-rr 66.4%

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

   if -1.65e-187 < B < -5.1e-231

   1. Initial program 72.5%

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

      1. associate-*l/ 72.5%

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

      2. *-lft-identity 72.5%

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

      3. +-commutative 72.5%

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

      4. unpow2 72.5%

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

      5. unpow2 72.5%

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

      6. hypot-def 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in A around -inf 72.2%

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

   if -1.55000000000000002e-294 < B < 2.1000000000000001e-307 or 5.1999999999999998e-252 < B < 3e-189

   1. Initial program 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*l/ 80.8%

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

      4. *-lft-identity 80.8%

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

      5. sub-neg 80.8%

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

      6. associate-+l- 80.7%

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

      7. sub-neg 80.7%

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

      8. remove-double-neg 80.7%

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

      9. +-commutative 80.7%

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

      10. unpow2 80.7%

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

      11. unpow2 80.7%

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

      12. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. neg-mul-1 80.6%

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

      2. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in C around inf 80.7%

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

   if 2.1000000000000001e-307 < B < 5.1999999999999998e-252 or 3e-189 < B < 8.9999999999999995e-104

   1. Initial program 36.5%

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

      1. associate-*r/ 36.5%

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

      2. unpow2 36.5%

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

   3. Simplified 36.5%

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

      1. *-commutative 36.5%

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

      2. associate--l- 32.5%

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

      3. +-commutative 32.5%

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

      4. unpow2 32.5%

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

      5. hypot-udef 58.7%

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

      6. div-inv 58.7%

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

      7. clear-num 58.7%

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

   5. Applied egg-rr 58.7%

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

   6. Taylor expanded in B around -inf 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

      3. sub-neg 62.6%

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

      4. +-commutative 62.6%

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

      5. distribute-neg-in 62.6%

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

      6. remove-double-neg 62.6%

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

      7. sub-neg 62.6%

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

   8. Simplified 62.6%

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

   if 8.9999999999999995e-104 < B

   1. Initial program 58.0%

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

      1. associate-*l/ 58.0%

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

      2. *-lft-identity 58.0%

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

      3. +-commutative 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-def 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in B around inf 81.0%

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

      1. neg-mul-1 81.0%

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

      2. unsub-neg 81.0%

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

   6. Simplified 81.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-294}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-104}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A - C}{B} + 1}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 46.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -7.6 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 335000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -7.6e-44)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.2e-191)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -1.7e-246)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -2.4e-294)
           (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
           (if (<= B 1.35e-307)
             t_1
             (if (<= B 9.2e-252)
               t_0
               (if (<= B 2.2e-187)
                 t_1
                 (if (<= B 2.2e-100)
                   t_0
                   (if (<= B 335000000000.0)
                     (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
                     (* 180.0 (/ (atan -1.0) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -7.6e-44) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.2e-191) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -1.7e-246) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -2.4e-294) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (B <= 1.35e-307) {
		tmp = t_1;
	} else if (B <= 9.2e-252) {
		tmp = t_0;
	} else if (B <= 2.2e-187) {
		tmp = t_1;
	} else if (B <= 2.2e-100) {
		tmp = t_0;
	} else if (B <= 335000000000.0) {
		tmp = 180.0 * (atan(((C * 2.0) / 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 t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -7.6e-44) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.2e-191) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -1.7e-246) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -2.4e-294) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (B <= 1.35e-307) {
		tmp = t_1;
	} else if (B <= 9.2e-252) {
		tmp = t_0;
	} else if (B <= 2.2e-187) {
		tmp = t_1;
	} else if (B <= 2.2e-100) {
		tmp = t_0;
	} else if (B <= 335000000000.0) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -7.6e-44:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.2e-191:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -1.7e-246:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -2.4e-294:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif B <= 1.35e-307:
		tmp = t_1
	elif B <= 9.2e-252:
		tmp = t_0
	elif B <= 2.2e-187:
		tmp = t_1
	elif B <= 2.2e-100:
		tmp = t_0
	elif B <= 335000000000.0:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -7.6e-44)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.2e-191)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -1.7e-246)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -2.4e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (B <= 1.35e-307)
		tmp = t_1;
	elseif (B <= 9.2e-252)
		tmp = t_0;
	elseif (B <= 2.2e-187)
		tmp = t_1;
	elseif (B <= 2.2e-100)
		tmp = t_0;
	elseif (B <= 335000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -7.6e-44)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.2e-191)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -1.7e-246)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -2.4e-294)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (B <= 1.35e-307)
		tmp = t_1;
	elseif (B <= 9.2e-252)
		tmp = t_0;
	elseif (B <= 2.2e-187)
		tmp = t_1;
	elseif (B <= 2.2e-100)
		tmp = t_0;
	elseif (B <= 335000000000.0)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7.6e-44], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.2e-191], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.7e-246], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.4e-294], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-307], t$95$1, If[LessEqual[B, 9.2e-252], t$95$0, If[LessEqual[B, 2.2e-187], t$95$1, If[LessEqual[B, 2.2e-100], t$95$0, If[LessEqual[B, 335000000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -7.6000000000000002e-44

   1. Initial program 58.6%

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

      1. associate-*l/ 58.6%

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

      2. *-lft-identity 58.6%

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

      3. +-commutative 58.6%

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

      4. unpow2 58.6%

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

      5. unpow2 58.6%

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

      6. hypot-def 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in B around -inf 63.3%

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

   if -7.6000000000000002e-44 < B < -8.2000000000000004e-191

   1. Initial program 41.6%

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

      1. associate-*r/ 41.6%

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

      2. unpow2 41.6%

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

   3. Simplified 41.6%

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

      1. *-commutative 41.6%

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

      2. associate--l- 41.5%

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

      3. +-commutative 41.5%

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

      4. unpow2 41.5%

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

      5. hypot-udef 58.3%

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

      6. div-inv 58.3%

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

      7. clear-num 58.3%

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

   5. Applied egg-rr 58.3%

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

   6. Taylor expanded in A around 0 39.7%

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

      1. unpow2 39.7%

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

      2. unpow2 39.7%

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

      3. hypot-def 56.5%

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

   8. Simplified 56.5%

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

   9. Taylor expanded in C around inf 49.7%

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

   10. Taylor expanded in B around 0 49.8%

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

   if -8.2000000000000004e-191 < B < -1.7000000000000001e-246

   1. Initial program 49.9%

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

      1. associate-*l/ 49.9%

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

      2. *-lft-identity 49.9%

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

      3. +-commutative 49.9%

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

      4. unpow2 49.9%

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

      5. unpow2 49.9%

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

      6. hypot-def 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in A around -inf 73.8%

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

   if -1.7000000000000001e-246 < B < -2.39999999999999997e-294

   1. Initial program 36.3%

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

      1. associate-*r/ 36.3%

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

      2. unpow2 36.3%

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

   3. Simplified 36.3%

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

      1. *-commutative 36.3%

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

      2. associate--l- 36.3%

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

      3. +-commutative 36.3%

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

      4. unpow2 36.3%

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

      5. hypot-udef 68.8%

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

      6. div-inv 68.8%

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

      7. clear-num 68.8%

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

   5. Applied egg-rr 68.8%

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

   6. Taylor expanded in A around 0 25.3%

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

      1. unpow2 25.3%

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

      2. unpow2 25.3%

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

      3. hypot-def 58.0%

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

   8. Simplified 58.0%

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

   9. Taylor expanded in C around inf 78.5%

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

   10. Taylor expanded in B around 0 78.4%

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

       1. associate-*r/ 78.4%

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

       2. associate-/l* 78.4%

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

       3. associate-/r/ 78.5%

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

   12. Simplified 78.5%

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

   if -2.39999999999999997e-294 < B < 1.34999999999999993e-307 or 9.1999999999999991e-252 < B < 2.20000000000000008e-187

   1. Initial program 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*l/ 80.8%

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

      4. *-lft-identity 80.8%

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

      5. sub-neg 80.8%

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

      6. associate-+l- 80.7%

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

      7. sub-neg 80.7%

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

      8. remove-double-neg 80.7%

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

      9. +-commutative 80.7%

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

      10. unpow2 80.7%

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

      11. unpow2 80.7%

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

      12. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. neg-mul-1 80.6%

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

      2. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in C around inf 80.7%

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

   if 1.34999999999999993e-307 < B < 9.1999999999999991e-252 or 2.20000000000000008e-187 < B < 2.19999999999999989e-100

   1. Initial program 36.5%

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

      1. associate-*l/ 36.5%

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

      2. *-lft-identity 36.5%

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

      3. +-commutative 36.5%

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

      4. unpow2 36.5%

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

      5. unpow2 36.5%

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

      6. hypot-def 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in C around inf 59.5%

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

      1. distribute-rgt1-in 59.5%

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

      2. metadata-eval 59.5%

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

      3. mul0-lft 59.5%

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

      4. metadata-eval 59.5%

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

   6. Simplified 59.5%

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

   if 2.19999999999999989e-100 < B < 3.35e11

   1. Initial program 69.2%

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

      1. associate-*l/ 69.2%

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

      2. *-lft-identity 69.2%

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

      3. +-commutative 69.2%

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

      4. unpow2 69.2%

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

      5. unpow2 69.2%

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

      6. hypot-def 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in C around -inf 43.2%

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

   if 3.35e11 < B

   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 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in B around inf 71.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.6 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 335000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 46.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -2.25 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 61000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -2.25e-44)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.2e-193)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -3.8e-246)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -1.45e-293)
           (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
           (if (<= B 9e-308)
             t_1
             (if (<= B 9.6e-251)
               t_0
               (if (<= B 2.3e-186)
                 t_1
                 (if (<= B 9.6e-104)
                   t_0
                   (if (<= B 61000000000.0)
                     (* (/ 180.0 PI) (atan (* 2.0 (/ C B))))
                     (* 180.0 (/ (atan -1.0) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -2.25e-44) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.2e-193) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -3.8e-246) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -1.45e-293) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (B <= 9e-308) {
		tmp = t_1;
	} else if (B <= 9.6e-251) {
		tmp = t_0;
	} else if (B <= 2.3e-186) {
		tmp = t_1;
	} else if (B <= 9.6e-104) {
		tmp = t_0;
	} else if (B <= 61000000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((2.0 * (C / B)));
	} 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((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -2.25e-44) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.2e-193) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -3.8e-246) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -1.45e-293) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (B <= 9e-308) {
		tmp = t_1;
	} else if (B <= 9.6e-251) {
		tmp = t_0;
	} else if (B <= 2.3e-186) {
		tmp = t_1;
	} else if (B <= 9.6e-104) {
		tmp = t_0;
	} else if (B <= 61000000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan((2.0 * (C / B)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -2.25e-44:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.2e-193:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -3.8e-246:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -1.45e-293:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif B <= 9e-308:
		tmp = t_1
	elif B <= 9.6e-251:
		tmp = t_0
	elif B <= 2.3e-186:
		tmp = t_1
	elif B <= 9.6e-104:
		tmp = t_0
	elif B <= 61000000000.0:
		tmp = (180.0 / math.pi) * math.atan((2.0 * (C / B)))
	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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -2.25e-44)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.2e-193)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -3.8e-246)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -1.45e-293)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (B <= 9e-308)
		tmp = t_1;
	elseif (B <= 9.6e-251)
		tmp = t_0;
	elseif (B <= 2.3e-186)
		tmp = t_1;
	elseif (B <= 9.6e-104)
		tmp = t_0;
	elseif (B <= 61000000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(2.0 * Float64(C / B))));
	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((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -2.25e-44)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.2e-193)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -3.8e-246)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -1.45e-293)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (B <= 9e-308)
		tmp = t_1;
	elseif (B <= 9.6e-251)
		tmp = t_0;
	elseif (B <= 2.3e-186)
		tmp = t_1;
	elseif (B <= 9.6e-104)
		tmp = t_0;
	elseif (B <= 61000000000.0)
		tmp = (180.0 / pi) * atan((2.0 * (C / B)));
	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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.25e-44], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.2e-193], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.8e-246], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.45e-293], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-308], t$95$1, If[LessEqual[B, 9.6e-251], t$95$0, If[LessEqual[B, 2.3e-186], t$95$1, If[LessEqual[B, 9.6e-104], t$95$0, If[LessEqual[B, 61000000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if B < -2.2499999999999999e-44

   1. Initial program 58.6%

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

      1. associate-*l/ 58.6%

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

      2. *-lft-identity 58.6%

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

      3. +-commutative 58.6%

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

      4. unpow2 58.6%

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

      5. unpow2 58.6%

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

      6. hypot-def 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in B around -inf 63.3%

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

   if -2.2499999999999999e-44 < B < -8.20000000000000005e-193

   1. Initial program 41.6%

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

      1. associate-*r/ 41.6%

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

      2. unpow2 41.6%

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

   3. Simplified 41.6%

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

      1. *-commutative 41.6%

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

      2. associate--l- 41.5%

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

      3. +-commutative 41.5%

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

      4. unpow2 41.5%

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

      5. hypot-udef 58.3%

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

      6. div-inv 58.3%

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

      7. clear-num 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 39.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 49.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 49.8%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -8.20000000000000005e-193 < B < -3.79999999999999976e-246

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 73.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -3.79999999999999976e-246 < B < -1.45e-293

   1. Initial program 36.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 36.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 36.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 68.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 58.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 58.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 78.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 78.4%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. associate-*r/ 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]

       2. associate-/l* 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)}}{\pi} \]

       3. associate-/r/ 78.5%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   12. Simplified 78.5%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{C} \cdot B\right)}{\pi}} \]

   if -1.45e-293 < B < 9.00000000000000017e-308 or 9.59999999999999984e-251 < B < 2.3000000000000001e-186

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 9.00000000000000017e-308 < B < 9.59999999999999984e-251 or 2.3000000000000001e-186 < B < 9.6000000000000003e-104

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 9.6000000000000003e-104 < B < 6.1e10

   1. Initial program 69.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 69.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 69.3%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 69.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 69.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 69.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 75.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in C around -inf 43.3%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{-1 \cdot C}}{B}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(-C\right)}}{B}\right) \]

   6. Simplified 43.3%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(-C\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 43.3%

      \[\leadsto \frac{180}{\pi} \cdot \color{blue}{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)} \]

   if 6.1e10 < B

   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 86.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 8 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.25 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-308}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 61000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(2 \cdot \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 59.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -4.2 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_2 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -4.2e-125)
     (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))
     (if (<= B -5.5e-194)
       t_1
       (if (<= B -8.2e-238)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -6.4e-292)
           t_1
           (if (<= B 2e-307)
             t_2
             (if (<= B 4.6e-252)
               t_0
               (if (<= B 1.05e-186)
                 t_2
                 (if (<= B 9e-104)
                   t_0
                   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_2 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -4.2e-125) {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	} else if (B <= -5.5e-194) {
		tmp = t_1;
	} else if (B <= -8.2e-238) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -6.4e-292) {
		tmp = t_1;
	} else if (B <= 2e-307) {
		tmp = t_2;
	} else if (B <= 4.6e-252) {
		tmp = t_0;
	} else if (B <= 1.05e-186) {
		tmp = t_2;
	} else if (B <= 9e-104) {
		tmp = t_0;
	} 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 t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double t_1 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_2 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -4.2e-125) {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	} else if (B <= -5.5e-194) {
		tmp = t_1;
	} else if (B <= -8.2e-238) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -6.4e-292) {
		tmp = t_1;
	} else if (B <= 2e-307) {
		tmp = t_2;
	} else if (B <= 4.6e-252) {
		tmp = t_0;
	} else if (B <= 1.05e-186) {
		tmp = t_2;
	} else if (B <= 9e-104) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_1 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_2 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -4.2e-125:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	elif B <= -5.5e-194:
		tmp = t_1
	elif B <= -8.2e-238:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -6.4e-292:
		tmp = t_1
	elif B <= 2e-307:
		tmp = t_2
	elif B <= 4.6e-252:
		tmp = t_0
	elif B <= 1.05e-186:
		tmp = t_2
	elif B <= 9e-104:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	t_1 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_2 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -4.2e-125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	elseif (B <= -5.5e-194)
		tmp = t_1;
	elseif (B <= -8.2e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -6.4e-292)
		tmp = t_1;
	elseif (B <= 2e-307)
		tmp = t_2;
	elseif (B <= 4.6e-252)
		tmp = t_0;
	elseif (B <= 1.05e-186)
		tmp = t_2;
	elseif (B <= 9e-104)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_2 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -4.2e-125)
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	elseif (B <= -5.5e-194)
		tmp = t_1;
	elseif (B <= -8.2e-238)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -6.4e-292)
		tmp = t_1;
	elseif (B <= 2e-307)
		tmp = t_2;
	elseif (B <= 4.6e-252)
		tmp = t_0;
	elseif (B <= 1.05e-186)
		tmp = t_2;
	elseif (B <= 9e-104)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((((C - 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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.2e-125], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.5e-194], t$95$1, If[LessEqual[B, -8.2e-238], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.4e-292], t$95$1, If[LessEqual[B, 2e-307], t$95$2, If[LessEqual[B, 4.6e-252], t$95$0, If[LessEqual[B, 1.05e-186], t$95$2, If[LessEqual[B, 9e-104], t$95$0, 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 6 regimes

2. if B < -4.2e-125

   1. Initial program 56.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 56.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 56.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 56.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 56.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 77.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   if -4.2e-125 < B < -5.49999999999999941e-194 or -8.2000000000000002e-238 < B < -6.4000000000000003e-292

   1. Initial program 29.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 29.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 29.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 29.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 59.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 57.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 66.1%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 66.1%

          \[\leadsto \color{blue}{1 \cdot \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

       2. associate-/l* 66.4%

          \[\leadsto 1 \cdot \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   11. Applied egg-rr 66.4%

       \[\leadsto \color{blue}{1 \cdot \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   if -5.49999999999999941e-194 < B < -8.2000000000000002e-238

   1. Initial program 72.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 86.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 72.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -6.4000000000000003e-292 < B < 1.99999999999999982e-307 or 4.5999999999999996e-252 < B < 1.0500000000000001e-186

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.99999999999999982e-307 < B < 4.5999999999999996e-252 or 1.0500000000000001e-186 < B < 8.9999999999999995e-104

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 8.9999999999999995e-104 < B

   1. Initial program 58.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-194}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 59.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.75 \cdot 10^{-294}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -3.6e-125)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -8.5e-195)
       t_0
       (if (<= B -4.4e-238)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -2.75e-294)
           t_0
           (if (<= B 1.6e-307)
             t_1
             (if (<= B 6.5e-252)
               t_2
               (if (<= B 2.6e-187)
                 t_1
                 (if (<= B 9.8e-104)
                   t_2
                   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -3.6e-125) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -8.5e-195) {
		tmp = t_0;
	} else if (B <= -4.4e-238) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -2.75e-294) {
		tmp = t_0;
	} else if (B <= 1.6e-307) {
		tmp = t_1;
	} else if (B <= 6.5e-252) {
		tmp = t_2;
	} else if (B <= 2.6e-187) {
		tmp = t_1;
	} else if (B <= 9.8e-104) {
		tmp = t_2;
	} 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 t_0 = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -3.6e-125) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -8.5e-195) {
		tmp = t_0;
	} else if (B <= -4.4e-238) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -2.75e-294) {
		tmp = t_0;
	} else if (B <= 1.6e-307) {
		tmp = t_1;
	} else if (B <= 6.5e-252) {
		tmp = t_2;
	} else if (B <= 2.6e-187) {
		tmp = t_1;
	} else if (B <= 9.8e-104) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -3.6e-125:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -8.5e-195:
		tmp = t_0
	elif B <= -4.4e-238:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -2.75e-294:
		tmp = t_0
	elif B <= 1.6e-307:
		tmp = t_1
	elif B <= 6.5e-252:
		tmp = t_2
	elif B <= 2.6e-187:
		tmp = t_1
	elif B <= 9.8e-104:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -3.6e-125)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -8.5e-195)
		tmp = t_0;
	elseif (B <= -4.4e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -2.75e-294)
		tmp = t_0;
	elseif (B <= 1.6e-307)
		tmp = t_1;
	elseif (B <= 6.5e-252)
		tmp = t_2;
	elseif (B <= 2.6e-187)
		tmp = t_1;
	elseif (B <= 9.8e-104)
		tmp = t_2;
	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)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -3.6e-125)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -8.5e-195)
		tmp = t_0;
	elseif (B <= -4.4e-238)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -2.75e-294)
		tmp = t_0;
	elseif (B <= 1.6e-307)
		tmp = t_1;
	elseif (B <= 6.5e-252)
		tmp = t_2;
	elseif (B <= 2.6e-187)
		tmp = t_1;
	elseif (B <= 9.8e-104)
		tmp = t_2;
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.6e-125], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.5e-195], t$95$0, If[LessEqual[B, -4.4e-238], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.75e-294], t$95$0, If[LessEqual[B, 1.6e-307], t$95$1, If[LessEqual[B, 6.5e-252], t$95$2, If[LessEqual[B, 2.6e-187], t$95$1, If[LessEqual[B, 9.8e-104], t$95$2, 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 6 regimes

2. if B < -3.6000000000000002e-125

   1. Initial program 56.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 56.7%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 56.7%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 56.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 56.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 56.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 56.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 56.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 56.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 56.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 56.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 56.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 81.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 77.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 77.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 77.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 77.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   if -3.6000000000000002e-125 < B < -8.50000000000000023e-195 or -4.39999999999999982e-238 < B < -2.75e-294

   1. Initial program 29.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 29.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 29.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 29.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 28.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 59.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 57.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 66.1%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 66.1%

          \[\leadsto \color{blue}{1 \cdot \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

       2. associate-/l* 66.4%

          \[\leadsto 1 \cdot \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   11. Applied egg-rr 66.4%

       \[\leadsto \color{blue}{1 \cdot \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   if -8.50000000000000023e-195 < B < -4.39999999999999982e-238

   1. Initial program 72.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 72.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 86.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 72.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -2.75e-294 < B < 1.60000000000000005e-307 or 6.4999999999999998e-252 < B < 2.5999999999999999e-187

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.60000000000000005e-307 < B < 6.4999999999999998e-252 or 2.5999999999999999e-187 < B < 9.8000000000000006e-104

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 9.8000000000000006e-104 < B

   1. Initial program 58.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.75 \cdot 10^{-294}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 46.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-199}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.56 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -9e-47)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3.5e-199)
       t_0
       (if (<= B -3.8e-246)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -7.6e-295)
           t_0
           (if (<= B 1.56e-307)
             t_1
             (if (<= B 1.35e-250)
               t_2
               (if (<= B 1.6e-189)
                 t_1
                 (if (<= B 4.8e-101)
                   t_2
                   (if (<= B 3.5e+14)
                     t_1
                     (* 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 t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -9e-47) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.5e-199) {
		tmp = t_0;
	} else if (B <= -3.8e-246) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -7.6e-295) {
		tmp = t_0;
	} else if (B <= 1.56e-307) {
		tmp = t_1;
	} else if (B <= 1.35e-250) {
		tmp = t_2;
	} else if (B <= 1.6e-189) {
		tmp = t_1;
	} else if (B <= 4.8e-101) {
		tmp = t_2;
	} else if (B <= 3.5e+14) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -9e-47) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.5e-199) {
		tmp = t_0;
	} else if (B <= -3.8e-246) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -7.6e-295) {
		tmp = t_0;
	} else if (B <= 1.56e-307) {
		tmp = t_1;
	} else if (B <= 1.35e-250) {
		tmp = t_2;
	} else if (B <= 1.6e-189) {
		tmp = t_1;
	} else if (B <= 4.8e-101) {
		tmp = t_2;
	} else if (B <= 3.5e+14) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -9e-47:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.5e-199:
		tmp = t_0
	elif B <= -3.8e-246:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -7.6e-295:
		tmp = t_0
	elif B <= 1.56e-307:
		tmp = t_1
	elif B <= 1.35e-250:
		tmp = t_2
	elif B <= 1.6e-189:
		tmp = t_1
	elif B <= 4.8e-101:
		tmp = t_2
	elif B <= 3.5e+14:
		tmp = t_1
	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))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -9e-47)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.5e-199)
		tmp = t_0;
	elseif (B <= -3.8e-246)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -7.6e-295)
		tmp = t_0;
	elseif (B <= 1.56e-307)
		tmp = t_1;
	elseif (B <= 1.35e-250)
		tmp = t_2;
	elseif (B <= 1.6e-189)
		tmp = t_1;
	elseif (B <= 4.8e-101)
		tmp = t_2;
	elseif (B <= 3.5e+14)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -9e-47)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.5e-199)
		tmp = t_0;
	elseif (B <= -3.8e-246)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -7.6e-295)
		tmp = t_0;
	elseif (B <= 1.56e-307)
		tmp = t_1;
	elseif (B <= 1.35e-250)
		tmp = t_2;
	elseif (B <= 1.6e-189)
		tmp = t_1;
	elseif (B <= 4.8e-101)
		tmp = t_2;
	elseif (B <= 3.5e+14)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9e-47], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.5e-199], t$95$0, If[LessEqual[B, -3.8e-246], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.6e-295], t$95$0, If[LessEqual[B, 1.56e-307], t$95$1, If[LessEqual[B, 1.35e-250], t$95$2, If[LessEqual[B, 1.6e-189], t$95$1, If[LessEqual[B, 4.8e-101], t$95$2, If[LessEqual[B, 3.5e+14], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -9e-47

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 87.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -9e-47 < B < -3.4999999999999999e-199 or -3.79999999999999976e-246 < B < -7.60000000000000037e-295

   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-*r/ 40.5%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 40.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 40.5%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 60.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 36.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 36.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 36.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 55.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 55.5%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -3.4999999999999999e-199 < B < -3.79999999999999976e-246

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 73.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -7.60000000000000037e-295 < B < 1.56e-307 or 1.35000000000000001e-250 < B < 1.6e-189 or 4.8e-101 < B < 3.5e14

   1. Initial program 73.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 73.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 74.0%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 73.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 73.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 80.4%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 65.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 65.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 65.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 65.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 58.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.56e-307 < B < 1.35000000000000001e-250 or 1.6e-189 < B < 4.8e-101

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 3.5e14 < B

   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 86.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.56 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 46.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.72 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 245000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -3.9e-44)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.8e-194)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -1.25e-245)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B -6.2e-293)
           (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
           (if (<= B 1.72e-307)
             t_1
             (if (<= B 2.8e-251)
               t_0
               (if (<= B 3.5e-187)
                 t_1
                 (if (<= B 2.9e-100)
                   t_0
                   (if (<= B 245000000000.0)
                     t_1
                     (* 180.0 (/ (atan -1.0) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -3.9e-44) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.8e-194) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -1.25e-245) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= -6.2e-293) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (B <= 1.72e-307) {
		tmp = t_1;
	} else if (B <= 2.8e-251) {
		tmp = t_0;
	} else if (B <= 3.5e-187) {
		tmp = t_1;
	} else if (B <= 2.9e-100) {
		tmp = t_0;
	} else if (B <= 245000000000.0) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -3.9e-44) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.8e-194) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -1.25e-245) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= -6.2e-293) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (B <= 1.72e-307) {
		tmp = t_1;
	} else if (B <= 2.8e-251) {
		tmp = t_0;
	} else if (B <= 3.5e-187) {
		tmp = t_1;
	} else if (B <= 2.9e-100) {
		tmp = t_0;
	} else if (B <= 245000000000.0) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -3.9e-44:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.8e-194:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -1.25e-245:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= -6.2e-293:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif B <= 1.72e-307:
		tmp = t_1
	elif B <= 2.8e-251:
		tmp = t_0
	elif B <= 3.5e-187:
		tmp = t_1
	elif B <= 2.9e-100:
		tmp = t_0
	elif B <= 245000000000.0:
		tmp = t_1
	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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -3.9e-44)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.8e-194)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -1.25e-245)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= -6.2e-293)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (B <= 1.72e-307)
		tmp = t_1;
	elseif (B <= 2.8e-251)
		tmp = t_0;
	elseif (B <= 3.5e-187)
		tmp = t_1;
	elseif (B <= 2.9e-100)
		tmp = t_0;
	elseif (B <= 245000000000.0)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -3.9e-44)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.8e-194)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -1.25e-245)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= -6.2e-293)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (B <= 1.72e-307)
		tmp = t_1;
	elseif (B <= 2.8e-251)
		tmp = t_0;
	elseif (B <= 3.5e-187)
		tmp = t_1;
	elseif (B <= 2.9e-100)
		tmp = t_0;
	elseif (B <= 245000000000.0)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.9e-44], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.8e-194], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.25e-245], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.2e-293], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.72e-307], t$95$1, If[LessEqual[B, 2.8e-251], t$95$0, If[LessEqual[B, 3.5e-187], t$95$1, If[LessEqual[B, 2.9e-100], t$95$0, If[LessEqual[B, 245000000000.0], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -3.9000000000000002e-44

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 87.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -3.9000000000000002e-44 < B < -2.80000000000000011e-194

   1. Initial program 41.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 41.6%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 41.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 39.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 49.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 49.8%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -2.80000000000000011e-194 < B < -1.2499999999999999e-245

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 73.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

   if -1.2499999999999999e-245 < B < -6.19999999999999965e-293

   1. Initial program 36.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 36.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 36.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 68.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 58.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 58.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 78.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 78.4%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. associate-*r/ 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]

       2. associate-/l* 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)}}{\pi} \]

       3. associate-/r/ 78.5%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   12. Simplified 78.5%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{C} \cdot B\right)}{\pi}} \]

   if -6.19999999999999965e-293 < B < 1.72000000000000008e-307 or 2.79999999999999989e-251 < B < 3.49999999999999979e-187 or 2.89999999999999975e-100 < B < 2.45e11

   1. Initial program 73.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 73.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 74.0%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 74.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 73.9%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 73.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 73.9%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 80.4%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 65.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 65.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 65.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 65.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 58.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.72000000000000008e-307 < B < 2.79999999999999989e-251 or 3.49999999999999979e-187 < B < 2.89999999999999975e-100

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 2.45e11 < B

   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 86.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 71.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.72 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 245000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 46.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{+23}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_2 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -1.3e-44)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3.2e-296)
       t_0
       (if (<= B 2.1e-307)
         t_2
         (if (<= B 2.7e-251)
           t_1
           (if (<= B 3.7e-187)
             t_2
             (if (<= B 2.7e-102)
               t_1
               (if (<= B 8.5e-33)
                 t_2
                 (if (<= B 6.5e+23) 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 t_1 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_2 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -1.3e-44) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.2e-296) {
		tmp = t_0;
	} else if (B <= 2.1e-307) {
		tmp = t_2;
	} else if (B <= 2.7e-251) {
		tmp = t_1;
	} else if (B <= 3.7e-187) {
		tmp = t_2;
	} else if (B <= 2.7e-102) {
		tmp = t_1;
	} else if (B <= 8.5e-33) {
		tmp = t_2;
	} else if (B <= 6.5e+23) {
		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 t_1 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double t_2 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -1.3e-44) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.2e-296) {
		tmp = t_0;
	} else if (B <= 2.1e-307) {
		tmp = t_2;
	} else if (B <= 2.7e-251) {
		tmp = t_1;
	} else if (B <= 3.7e-187) {
		tmp = t_2;
	} else if (B <= 2.7e-102) {
		tmp = t_1;
	} else if (B <= 8.5e-33) {
		tmp = t_2;
	} else if (B <= 6.5e+23) {
		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)
	t_1 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_2 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -1.3e-44:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.2e-296:
		tmp = t_0
	elif B <= 2.1e-307:
		tmp = t_2
	elif B <= 2.7e-251:
		tmp = t_1
	elif B <= 3.7e-187:
		tmp = t_2
	elif B <= 2.7e-102:
		tmp = t_1
	elif B <= 8.5e-33:
		tmp = t_2
	elif B <= 6.5e+23:
		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))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	t_2 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -1.3e-44)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.2e-296)
		tmp = t_0;
	elseif (B <= 2.1e-307)
		tmp = t_2;
	elseif (B <= 2.7e-251)
		tmp = t_1;
	elseif (B <= 3.7e-187)
		tmp = t_2;
	elseif (B <= 2.7e-102)
		tmp = t_1;
	elseif (B <= 8.5e-33)
		tmp = t_2;
	elseif (B <= 6.5e+23)
		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);
	t_1 = 180.0 * (atan((0.0 / B)) / pi);
	t_2 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -1.3e-44)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.2e-296)
		tmp = t_0;
	elseif (B <= 2.1e-307)
		tmp = t_2;
	elseif (B <= 2.7e-251)
		tmp = t_1;
	elseif (B <= 3.7e-187)
		tmp = t_2;
	elseif (B <= 2.7e-102)
		tmp = t_1;
	elseif (B <= 8.5e-33)
		tmp = t_2;
	elseif (B <= 6.5e+23)
		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]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.3e-44], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.2e-296], t$95$0, If[LessEqual[B, 2.1e-307], t$95$2, If[LessEqual[B, 2.7e-251], t$95$1, If[LessEqual[B, 3.7e-187], t$95$2, If[LessEqual[B, 2.7e-102], t$95$1, If[LessEqual[B, 8.5e-33], t$95$2, If[LessEqual[B, 6.5e+23], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.2999999999999999e-44

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 87.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.2999999999999999e-44 < B < -3.20000000000000013e-296 or 8.49999999999999945e-33 < B < 6.4999999999999996e23

   1. Initial program 44.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 44.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 44.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 44.8%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 39.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 39.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 39.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 47.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 47.7%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -3.20000000000000013e-296 < B < 2.1000000000000001e-307 or 2.7000000000000001e-251 < B < 3.7000000000000001e-187 or 2.7e-102 < B < 8.49999999999999945e-33

   1. Initial program 78.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 78.6%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 78.6%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 78.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 78.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 78.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 85.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 74.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 74.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 74.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 74.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 67.4%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 2.1000000000000001e-307 < B < 2.7000000000000001e-251 or 3.7000000000000001e-187 < B < 2.7e-102

   1. Initial program 36.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 36.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 81.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 59.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 59.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 6.4999999999999996e23 < B

   1. Initial program 55.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 55.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 55.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 55.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 55.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 55.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 89.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 73.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{+23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 52.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -1.52e-46)
     (* (/ 180.0 PI) (atan (/ (- B A) B)))
     (if (<= B -9.5e-193)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -1.3e-245)
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
         (if (<= B -5.6e-294)
           (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
           (if (<= B 1.95e-307)
             t_1
             (if (<= B 9.5e-251)
               t_0
               (if (<= B 2e-189)
                 t_1
                 (if (<= B 4.8e-106)
                   t_0
                   (/ (* -180.0 (atan (/ (+ B A) B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -1.52e-46) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else if (B <= -9.5e-193) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -1.3e-245) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (B <= -5.6e-294) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (B <= 1.95e-307) {
		tmp = t_1;
	} else if (B <= 9.5e-251) {
		tmp = t_0;
	} else if (B <= 2e-189) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = t_0;
	} 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((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -1.52e-46) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else if (B <= -9.5e-193) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -1.3e-245) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (B <= -5.6e-294) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (B <= 1.95e-307) {
		tmp = t_1;
	} else if (B <= 9.5e-251) {
		tmp = t_0;
	} else if (B <= 2e-189) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = t_0;
	} 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((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -1.52e-46:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	elif B <= -9.5e-193:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -1.3e-245:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif B <= -5.6e-294:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif B <= 1.95e-307:
		tmp = t_1
	elif B <= 9.5e-251:
		tmp = t_0
	elif B <= 2e-189:
		tmp = t_1
	elif B <= 4.8e-106:
		tmp = t_0
	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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -1.52e-46)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	elseif (B <= -9.5e-193)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -1.3e-245)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (B <= -5.6e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (B <= 1.95e-307)
		tmp = t_1;
	elseif (B <= 9.5e-251)
		tmp = t_0;
	elseif (B <= 2e-189)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = t_0;
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -1.52e-46)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	elseif (B <= -9.5e-193)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -1.3e-245)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (B <= -5.6e-294)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (B <= 1.95e-307)
		tmp = t_1;
	elseif (B <= 9.5e-251)
		tmp = t_0;
	elseif (B <= 2e-189)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = t_0;
	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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.52e-46], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-193], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.3e-245], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.6e-294], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-307], t$95$1, If[LessEqual[B, 9.5e-251], t$95$0, If[LessEqual[B, 2e-189], t$95$1, If[LessEqual[B, 4.8e-106], t$95$0, N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -1.52000000000000006e-46

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 58.6%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 77.4%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)} \]

   if -1.52000000000000006e-46 < B < -9.5000000000000003e-193

   1. Initial program 41.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 41.6%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 41.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 39.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 49.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 49.8%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -9.5000000000000003e-193 < B < -1.30000000000000003e-245

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{{B}^{2}}{A}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}}{B}\right)}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{B \cdot B}{A}}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 73.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]
   8. Step-by-step derivation

      1. associate-*r/ 73.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]

      2. associate-/l* 76.0%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   9. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   if -1.30000000000000003e-245 < B < -5.59999999999999981e-294

   1. Initial program 36.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 36.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 36.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 68.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 58.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 58.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 78.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 78.4%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. associate-*r/ 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]

       2. associate-/l* 78.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)}}{\pi} \]

       3. associate-/r/ 78.5%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   12. Simplified 78.5%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{C} \cdot B\right)}{\pi}} \]

   if -5.59999999999999981e-294 < B < 1.95e-307 or 9.49999999999999927e-251 < B < 2.00000000000000014e-189

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.95e-307 < B < 9.49999999999999927e-251 or 2.00000000000000014e-189 < B < 4.7999999999999995e-106

   1. Initial program 37.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 84.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 4.7999999999999995e-106 < B

   1. Initial program 57.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 57.4%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 82.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in C around 0 50.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. associate-*r/ 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}{B}\right)}}{\pi} \]

      2. mul-1-neg 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}{B}\right)}{\pi} \]

      3. +-commutative 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}{B}\right)}{\pi} \]

      4. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      5. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      6. hypot-def 72.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}{\pi} \]

   8. Simplified 72.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 1.6%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)\right)}}{\pi} \]

      2. expm1-udef 1.6%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)} - 1}}{\pi} \]

      3. distribute-frac-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1}{\pi} \]

      4. atan-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1}{\pi} \]

   10. Applied egg-rr 1.6%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1}}{\pi} \]
   11. Step-by-step derivation

       1. expm1-def 1.6%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 72.7%

          \[\leadsto \frac{\color{blue}{180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}}{\pi} \]

       3. distribute-rgt-neg-out 72.7%

          \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       4. distribute-lft-neg-in 72.7%

          \[\leadsto \frac{\color{blue}{\left(-180\right) \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       5. metadata-eval 72.7%

          \[\leadsto \frac{\color{blue}{-180} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi} \]

   12. Simplified 72.7%

       \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

   13. Taylor expanded in A around 0 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{A + B}}{B}\right)}{\pi} \]
   14. Step-by-step derivation

       1. +-commutative 70.9%

          \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]

   15. Simplified 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18: 52.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -6.6 \cdot 10^{-294}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -2.55e-45)
     (* (/ 180.0 PI) (atan (/ (- B A) B)))
     (if (<= B -6.4e-196)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -1.9e-246)
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
         (if (<= B -6.6e-294)
           (/ (* 180.0 (atan (* B (/ -0.5 C)))) PI)
           (if (<= B 1.05e-307)
             t_1
             (if (<= B 5.2e-252)
               t_0
               (if (<= B 2.5e-186)
                 t_1
                 (if (<= B 4.8e-106)
                   t_0
                   (/ (* -180.0 (atan (/ (+ B A) B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -2.55e-45) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else if (B <= -6.4e-196) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -1.9e-246) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (B <= -6.6e-294) {
		tmp = (180.0 * atan((B * (-0.5 / C)))) / ((double) M_PI);
	} else if (B <= 1.05e-307) {
		tmp = t_1;
	} else if (B <= 5.2e-252) {
		tmp = t_0;
	} else if (B <= 2.5e-186) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = t_0;
	} 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((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -2.55e-45) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else if (B <= -6.4e-196) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -1.9e-246) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (B <= -6.6e-294) {
		tmp = (180.0 * Math.atan((B * (-0.5 / C)))) / Math.PI;
	} else if (B <= 1.05e-307) {
		tmp = t_1;
	} else if (B <= 5.2e-252) {
		tmp = t_0;
	} else if (B <= 2.5e-186) {
		tmp = t_1;
	} else if (B <= 4.8e-106) {
		tmp = t_0;
	} 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((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -2.55e-45:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	elif B <= -6.4e-196:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -1.9e-246:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif B <= -6.6e-294:
		tmp = (180.0 * math.atan((B * (-0.5 / C)))) / math.pi
	elif B <= 1.05e-307:
		tmp = t_1
	elif B <= 5.2e-252:
		tmp = t_0
	elif B <= 2.5e-186:
		tmp = t_1
	elif B <= 4.8e-106:
		tmp = t_0
	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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -2.55e-45)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	elseif (B <= -6.4e-196)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -1.9e-246)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (B <= -6.6e-294)
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(-0.5 / C)))) / pi);
	elseif (B <= 1.05e-307)
		tmp = t_1;
	elseif (B <= 5.2e-252)
		tmp = t_0;
	elseif (B <= 2.5e-186)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = t_0;
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -2.55e-45)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	elseif (B <= -6.4e-196)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -1.9e-246)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (B <= -6.6e-294)
		tmp = (180.0 * atan((B * (-0.5 / C)))) / pi;
	elseif (B <= 1.05e-307)
		tmp = t_1;
	elseif (B <= 5.2e-252)
		tmp = t_0;
	elseif (B <= 2.5e-186)
		tmp = t_1;
	elseif (B <= 4.8e-106)
		tmp = t_0;
	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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.55e-45], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.4e-196], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.9e-246], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.6e-294], N[(N[(180.0 * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-307], t$95$1, If[LessEqual[B, 5.2e-252], t$95$0, If[LessEqual[B, 2.5e-186], t$95$1, If[LessEqual[B, 4.8e-106], t$95$0, N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -2.5499999999999999e-45

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 58.6%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 77.4%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)} \]

   if -2.5499999999999999e-45 < B < -6.3999999999999999e-196

   1. Initial program 41.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 41.6%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 41.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 41.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 39.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 49.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 49.8%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -6.3999999999999999e-196 < B < -1.89999999999999988e-246

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{{B}^{2}}{A}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}}{B}\right)}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{B \cdot B}{A}}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 73.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]
   8. Step-by-step derivation

      1. associate-*r/ 73.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]

      2. associate-/l* 76.0%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   9. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   if -1.89999999999999988e-246 < B < -6.6e-294

   1. Initial program 36.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 36.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 36.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 36.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 68.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 68.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 25.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 25.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 58.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 58.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 78.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 78.5%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\right)\right)}}{\pi} \]

       2. expm1-udef 47.2%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\right)} - 1}}{\pi} \]

   11. Applied egg-rr 47.2%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\right)} - 1}}{\pi} \]
   12. Step-by-step derivation

       1. expm1-def 78.5%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 78.5%

          \[\leadsto \frac{\color{blue}{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

       3. associate-*r/ 78.5%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)}}{\pi} \]

       4. associate-/l* 78.5%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)}}{\pi} \]

       5. associate-/r/ 78.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   13. Simplified 78.7%

       \[\leadsto \frac{\color{blue}{180 \cdot \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right)}}{\pi} \]

   if -6.6e-294 < B < 1.0500000000000001e-307 or 5.1999999999999998e-252 < B < 2.5e-186

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.0500000000000001e-307 < B < 5.1999999999999998e-252 or 2.5e-186 < B < 4.7999999999999995e-106

   1. Initial program 37.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 84.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 4.7999999999999995e-106 < B

   1. Initial program 57.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 57.4%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 82.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in C around 0 50.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. associate-*r/ 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}{B}\right)}}{\pi} \]

      2. mul-1-neg 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}{B}\right)}{\pi} \]

      3. +-commutative 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}{B}\right)}{\pi} \]

      4. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      5. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      6. hypot-def 72.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}{\pi} \]

   8. Simplified 72.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 1.6%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)\right)}}{\pi} \]

      2. expm1-udef 1.6%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)} - 1}}{\pi} \]

      3. distribute-frac-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1}{\pi} \]

      4. atan-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1}{\pi} \]

   10. Applied egg-rr 1.6%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1}}{\pi} \]
   11. Step-by-step derivation

       1. expm1-def 1.6%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 72.7%

          \[\leadsto \frac{\color{blue}{180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}}{\pi} \]

       3. distribute-rgt-neg-out 72.7%

          \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       4. distribute-lft-neg-in 72.7%

          \[\leadsto \frac{\color{blue}{\left(-180\right) \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       5. metadata-eval 72.7%

          \[\leadsto \frac{\color{blue}{-180} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi} \]

   12. Simplified 72.7%

       \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

   13. Taylor expanded in A around 0 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{A + B}}{B}\right)}{\pi} \]
   14. Step-by-step derivation

       1. +-commutative 70.9%

          \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]

   15. Simplified 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -6.4 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -6.6 \cdot 10^{-294}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19: 52.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-199}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-297}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))
        (t_1 (* (/ 180.0 PI) (atan (/ C B))))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -2.3e-45)
     (* (/ 180.0 PI) (atan (/ (- B A) B)))
     (if (<= B -3.6e-199)
       t_0
       (if (<= B -1.15e-245)
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
         (if (<= B -7e-297)
           t_0
           (if (<= B 1.15e-307)
             t_1
             (if (<= B 4e-251)
               t_2
               (if (<= B 1.15e-188)
                 t_1
                 (if (<= B 7e-106)
                   t_2
                   (/ (* -180.0 (atan (/ (+ B A) B))) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.3e-45) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else if (B <= -3.6e-199) {
		tmp = t_0;
	} else if (B <= -1.15e-245) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (B <= -7e-297) {
		tmp = t_0;
	} else if (B <= 1.15e-307) {
		tmp = t_1;
	} else if (B <= 4e-251) {
		tmp = t_2;
	} else if (B <= 1.15e-188) {
		tmp = t_1;
	} else if (B <= 7e-106) {
		tmp = t_2;
	} 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.PI / Math.atan((-0.5 * (B / C))));
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -2.3e-45) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else if (B <= -3.6e-199) {
		tmp = t_0;
	} else if (B <= -1.15e-245) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (B <= -7e-297) {
		tmp = t_0;
	} else if (B <= 1.15e-307) {
		tmp = t_1;
	} else if (B <= 4e-251) {
		tmp = t_2;
	} else if (B <= 1.15e-188) {
		tmp = t_1;
	} else if (B <= 7e-106) {
		tmp = t_2;
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -2.3e-45:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	elif B <= -3.6e-199:
		tmp = t_0
	elif B <= -1.15e-245:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif B <= -7e-297:
		tmp = t_0
	elif B <= 1.15e-307:
		tmp = t_1
	elif B <= 4e-251:
		tmp = t_2
	elif B <= 1.15e-188:
		tmp = t_1
	elif B <= 7e-106:
		tmp = t_2
	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(pi / atan(Float64(-0.5 * Float64(B / C)))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -2.3e-45)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	elseif (B <= -3.6e-199)
		tmp = t_0;
	elseif (B <= -1.15e-245)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (B <= -7e-297)
		tmp = t_0;
	elseif (B <= 1.15e-307)
		tmp = t_1;
	elseif (B <= 4e-251)
		tmp = t_2;
	elseif (B <= 1.15e-188)
		tmp = t_1;
	elseif (B <= 7e-106)
		tmp = t_2;
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan((-0.5 * (B / C))));
	t_1 = (180.0 / pi) * atan((C / B));
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -2.3e-45)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	elseif (B <= -3.6e-199)
		tmp = t_0;
	elseif (B <= -1.15e-245)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (B <= -7e-297)
		tmp = t_0;
	elseif (B <= 1.15e-307)
		tmp = t_1;
	elseif (B <= 4e-251)
		tmp = t_2;
	elseif (B <= 1.15e-188)
		tmp = t_1;
	elseif (B <= 7e-106)
		tmp = t_2;
	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[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.3e-45], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.6e-199], t$95$0, If[LessEqual[B, -1.15e-245], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7e-297], t$95$0, If[LessEqual[B, 1.15e-307], t$95$1, If[LessEqual[B, 4e-251], t$95$2, If[LessEqual[B, 1.15e-188], t$95$1, If[LessEqual[B, 7e-106], t$95$2, N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -2.29999999999999992e-45

   1. Initial program 58.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 58.6%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 58.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 58.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 86.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 86.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 77.4%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)} \]

   if -2.29999999999999992e-45 < B < -3.6000000000000002e-199 or -1.1500000000000001e-245 < B < -6.9999999999999998e-297

   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-*r/ 40.5%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 40.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 40.5%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 40.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 60.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 60.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 36.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 36.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 36.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 56.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 56.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 55.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 55.5%

          \[\leadsto \color{blue}{1 \cdot \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

       2. associate-/l* 55.7%

          \[\leadsto 1 \cdot \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   11. Applied egg-rr 55.7%

       \[\leadsto \color{blue}{1 \cdot \frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

   if -3.6000000000000002e-199 < B < -1.1500000000000001e-245

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{{B}^{2}}{A}}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{\color{blue}{B \cdot B}}{A}}{B}\right)}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0.5 \cdot \frac{B \cdot B}{A}}}{B}\right)}{\pi} \]

   7. Taylor expanded in B around 0 73.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]
   8. Step-by-step derivation

      1. associate-*r/ 73.9%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}} \]

      2. associate-/l* 76.0%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   9. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}} \]

   if -6.9999999999999998e-297 < B < 1.1499999999999999e-307 or 4.00000000000000006e-251 < B < 1.15e-188

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.1499999999999999e-307 < B < 4.00000000000000006e-251 or 1.15e-188 < B < 7e-106

   1. Initial program 37.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 37.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 84.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 61.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 7e-106 < B

   1. Initial program 57.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 57.4%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 57.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 82.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 82.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in C around 0 50.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. associate-*r/ 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}{B}\right)}}{\pi} \]

      2. mul-1-neg 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}{B}\right)}{\pi} \]

      3. +-commutative 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}{B}\right)}{\pi} \]

      4. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      5. unpow2 50.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      6. hypot-def 72.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}{\pi} \]

   8. Simplified 72.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 1.6%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)\right)}}{\pi} \]

      2. expm1-udef 1.6%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)} - 1}}{\pi} \]

      3. distribute-frac-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1}{\pi} \]

      4. atan-neg 1.6%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1}{\pi} \]

   10. Applied egg-rr 1.6%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1}}{\pi} \]
   11. Step-by-step derivation

       1. expm1-def 1.6%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 72.7%

          \[\leadsto \frac{\color{blue}{180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}}{\pi} \]

       3. distribute-rgt-neg-out 72.7%

          \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       4. distribute-lft-neg-in 72.7%

          \[\leadsto \frac{\color{blue}{\left(-180\right) \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       5. metadata-eval 72.7%

          \[\leadsto \frac{\color{blue}{-180} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi} \]

   12. Simplified 72.7%

       \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

   13. Taylor expanded in A around 0 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{A + B}}{B}\right)}{\pi} \]
   14. Step-by-step derivation

       1. +-commutative 70.9%

          \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]

   15. Simplified 70.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-297}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20: 63.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (/ (* 180.0 (atan (/ 1.0 (+ (* 2.0 (/ A B)) (* -2.0 (/ C B)))))) PI)))
   (if (<= B -3.2e-59)
     (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
     (if (<= B -5.6e-297)
       t_0
       (if (<= B 1.25e-307)
         (* (/ 180.0 PI) (atan (/ C B)))
         (if (<= B 8.4e-102)
           t_0
           (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / ((double) M_PI);
	double tmp;
	if (B <= -3.2e-59) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= -5.6e-297) {
		tmp = t_0;
	} else if (B <= 1.25e-307) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (B <= 8.4e-102) {
		tmp = t_0;
	} 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 t_0 = (180.0 * Math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / Math.PI;
	double tmp;
	if (B <= -3.2e-59) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= -5.6e-297) {
		tmp = t_0;
	} else if (B <= 1.25e-307) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (B <= 8.4e-102) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / math.pi
	tmp = 0
	if B <= -3.2e-59:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= -5.6e-297:
		tmp = t_0
	elif B <= 1.25e-307:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif B <= 8.4e-102:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(2.0 * Float64(A / B)) + Float64(-2.0 * Float64(C / B)))))) / pi)
	tmp = 0.0
	if (B <= -3.2e-59)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= -5.6e-297)
		tmp = t_0;
	elseif (B <= 1.25e-307)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (B <= 8.4e-102)
		tmp = t_0;
	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)
	t_0 = (180.0 * atan((1.0 / ((2.0 * (A / B)) + (-2.0 * (C / B)))))) / pi;
	tmp = 0.0;
	if (B <= -3.2e-59)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= -5.6e-297)
		tmp = t_0;
	elseif (B <= 1.25e-307)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (B <= 8.4e-102)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -3.2e-59], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.6e-297], t$95$0, If[LessEqual[B, 1.25e-307], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.4e-102], t$95$0, 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 4 regimes

2. if B < -3.1999999999999999e-59

   1. Initial program 58.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.3%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 58.3%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 58.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 58.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 58.3%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 58.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 58.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 58.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 58.2%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 58.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 58.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 86.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   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%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   if -3.1999999999999999e-59 < B < -5.59999999999999968e-297 or 1.25000000000000003e-307 < B < 8.4e-102

   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-*r/ 43.5%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 43.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 39.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 59.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around -inf 62.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{\color{blue}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}}\right)}{\pi} \]

   if -5.59999999999999968e-297 < B < 1.25000000000000003e-307

   1. Initial program 100.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 100.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 100.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 100.0%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 100.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 100.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 100.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 100.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 8.4e-102 < B

   1. Initial program 58.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 58.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 81.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 81.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 8.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B} + -2 \cdot \frac{C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 21: 45.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.08 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -1.55e-183)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1.08e-296)
       t_0
       (if (<= B 1.15e-307)
         t_1
         (if (<= B 3.2e-251)
           t_0
           (if (<= B 3.7e-187)
             t_1
             (if (<= B 1.95e-104) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -1.55e-183) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.08e-296) {
		tmp = t_0;
	} else if (B <= 1.15e-307) {
		tmp = t_1;
	} else if (B <= 3.2e-251) {
		tmp = t_0;
	} else if (B <= 3.7e-187) {
		tmp = t_1;
	} else if (B <= 1.95e-104) {
		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((0.0 / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -1.55e-183) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.08e-296) {
		tmp = t_0;
	} else if (B <= 1.15e-307) {
		tmp = t_1;
	} else if (B <= 3.2e-251) {
		tmp = t_0;
	} else if (B <= 3.7e-187) {
		tmp = t_1;
	} else if (B <= 1.95e-104) {
		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((0.0 / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -1.55e-183:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.08e-296:
		tmp = t_0
	elif B <= 1.15e-307:
		tmp = t_1
	elif B <= 3.2e-251:
		tmp = t_0
	elif B <= 3.7e-187:
		tmp = t_1
	elif B <= 1.95e-104:
		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(0.0 / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -1.55e-183)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.08e-296)
		tmp = t_0;
	elseif (B <= 1.15e-307)
		tmp = t_1;
	elseif (B <= 3.2e-251)
		tmp = t_0;
	elseif (B <= 3.7e-187)
		tmp = t_1;
	elseif (B <= 1.95e-104)
		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((0.0 / B)) / pi);
	t_1 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -1.55e-183)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.08e-296)
		tmp = t_0;
	elseif (B <= 1.15e-307)
		tmp = t_1;
	elseif (B <= 3.2e-251)
		tmp = t_0;
	elseif (B <= 3.7e-187)
		tmp = t_1;
	elseif (B <= 1.95e-104)
		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[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.55e-183], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.08e-296], t$95$0, If[LessEqual[B, 1.15e-307], t$95$1, If[LessEqual[B, 3.2e-251], t$95$0, If[LessEqual[B, 3.7e-187], t$95$1, If[LessEqual[B, 1.95e-104], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.55e-183

   1. Initial program 54.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 51.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.55e-183 < B < -1.08e-296 or 1.1499999999999999e-307 < B < 3.19999999999999982e-251 or 3.7000000000000001e-187 < B < 1.9500000000000001e-104

   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 80.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if -1.08e-296 < B < 1.1499999999999999e-307 or 3.19999999999999982e-251 < B < 3.7000000000000001e-187

   1. Initial program 80.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 80.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 80.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 80.7%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 87.2%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 80.6%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 80.6%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around inf 80.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)} \]

   if 1.9500000000000001e-104 < B

   1. Initial program 57.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 82.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 59.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.08 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 60.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -7.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -1.65 \cdot 10^{-282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.38 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* -180.0 (atan (/ (+ B A) B))) PI))
        (t_1 (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))))
   (if (<= C -7.6e+47)
     t_1
     (if (<= C -1.15e+25)
       t_0
       (if (<= C -1e-182)
         t_1
         (if (<= C -1.65e-282)
           t_0
           (if (<= C 1.38e-73)
             (* (/ 180.0 PI) (atan (/ (- B A) B)))
             (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (-180.0 * atan(((B + A) / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	double tmp;
	if (C <= -7.6e+47) {
		tmp = t_1;
	} else if (C <= -1.15e+25) {
		tmp = t_0;
	} else if (C <= -1e-182) {
		tmp = t_1;
	} else if (C <= -1.65e-282) {
		tmp = t_0;
	} else if (C <= 1.38e-73) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	double tmp;
	if (C <= -7.6e+47) {
		tmp = t_1;
	} else if (C <= -1.15e+25) {
		tmp = t_0;
	} else if (C <= -1e-182) {
		tmp = t_1;
	} else if (C <= -1.65e-282) {
		tmp = t_0;
	} else if (C <= 1.38e-73) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-180.0 * math.atan(((B + A) / B))) / math.pi
	t_1 = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	tmp = 0
	if C <= -7.6e+47:
		tmp = t_1
	elif C <= -1.15e+25:
		tmp = t_0
	elif C <= -1e-182:
		tmp = t_1
	elif C <= -1.65e-282:
		tmp = t_0
	elif C <= 1.38e-73:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi))
	tmp = 0.0
	if (C <= -7.6e+47)
		tmp = t_1;
	elseif (C <= -1.15e+25)
		tmp = t_0;
	elseif (C <= -1e-182)
		tmp = t_1;
	elseif (C <= -1.65e-282)
		tmp = t_0;
	elseif (C <= 1.38e-73)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (-180.0 * atan(((B + A) / B))) / pi;
	t_1 = 180.0 * (atan((((B + C) - A) / B)) / pi);
	tmp = 0.0;
	if (C <= -7.6e+47)
		tmp = t_1;
	elseif (C <= -1.15e+25)
		tmp = t_0;
	elseif (C <= -1e-182)
		tmp = t_1;
	elseif (C <= -1.65e-282)
		tmp = t_0;
	elseif (C <= 1.38e-73)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7.6e+47], t$95$1, If[LessEqual[C, -1.15e+25], t$95$0, If[LessEqual[C, -1e-182], t$95$1, If[LessEqual[C, -1.65e-282], t$95$0, If[LessEqual[C, 1.38e-73], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -7.6000000000000007e47 or -1.1499999999999999e25 < C < -1e-182

   1. Initial program 79.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 79.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 94.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 79.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + B\right) - A}}{B}\right)}{\pi} \]

   if -7.6000000000000007e47 < C < -1.1499999999999999e25 or -1e-182 < C < -1.65e-282

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 55.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 55.8%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 53.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 53.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 53.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 82.1%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 82.1%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 82.1%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 82.1%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in C around 0 55.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{B}^{2} + {A}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}{B}\right)}}{\pi} \]

      2. mul-1-neg 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{B}^{2} + {A}^{2}}\right)}}{B}\right)}{\pi} \]

      3. +-commutative 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{{A}^{2} + {B}^{2}}}\right)}{B}\right)}{\pi} \]

      4. unpow2 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      5. unpow2 55.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      6. hypot-def 89.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}{\pi} \]

   8. Simplified 89.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 35.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)\right)}}{\pi} \]

      2. expm1-udef 35.5%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\right)} - 1}}{\pi} \]

      3. distribute-frac-neg 35.5%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1}{\pi} \]

      4. atan-neg 35.5%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1}{\pi} \]

   10. Applied egg-rr 35.5%

       \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1}}{\pi} \]
   11. Step-by-step derivation

       1. expm1-def 35.5%

          \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)}}{\pi} \]

       2. expm1-log1p 89.8%

          \[\leadsto \frac{\color{blue}{180 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}}{\pi} \]

       3. distribute-rgt-neg-out 89.8%

          \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       4. distribute-lft-neg-in 89.8%

          \[\leadsto \frac{\color{blue}{\left(-180\right) \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

       5. metadata-eval 89.8%

          \[\leadsto \frac{\color{blue}{-180} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi} \]

   12. Simplified 89.8%

       \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}}{\pi} \]

   13. Taylor expanded in A around 0 63.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{A + B}}{B}\right)}{\pi} \]
   14. Step-by-step derivation

       1. +-commutative 63.9%

          \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]

   15. Simplified 63.9%

       \[\leadsto \frac{-180 \cdot \tan^{-1} \left(\frac{\color{blue}{B + A}}{B}\right)}{\pi} \]

   if -1.65e-282 < C < 1.37999999999999996e-73

   1. Initial program 62.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 62.0%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 62.0%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 62.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 62.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 62.0%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 61.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 61.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 61.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 61.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 61.8%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 61.8%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 77.6%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 57.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 57.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 57.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 57.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 57.2%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)} \]

   if 1.37999999999999996e-73 < C

   1. Initial program 22.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 22.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 22.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 22.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 24.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 24.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 24.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 59.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 63.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.6 \cdot 10^{+47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.65 \cdot 10^{-282}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.38 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 23: 56.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.4e+79)
   (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
   (if (<= C 1.5e-72)
     (* (/ 180.0 PI) (atan (/ (- B A) B)))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e+79) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (C <= 1.5e-72) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B - A) / B));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e+79) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (C <= 1.5e-72) {
		tmp = (180.0 / Math.PI) * Math.atan(((B - A) / B));
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.4e+79:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif C <= 1.5e-72:
		tmp = (180.0 / math.pi) * math.atan(((B - A) / B))
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.4e+79)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (C <= 1.5e-72)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B - A) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.4e+79)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (C <= 1.5e-72)
		tmp = (180.0 / pi) * atan(((B - A) / B));
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.4e+79], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.5e-72], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.4000000000000001e79

   1. Initial program 87.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 87.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 87.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 87.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 87.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 97.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around -inf 82.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{2 \cdot C}}{B}\right)}{\pi} \]

   if -1.4000000000000001e79 < C < 1.5e-72

   1. Initial program 63.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 63.7%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 63.7%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]

      3. associate-*l/ 63.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

      4. *-lft-identity 63.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \]

      5. sub-neg 63.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right) \]

      6. associate-+l- 62.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A - \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}{B}\right) \]

      7. sub-neg 62.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + \left(-\left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)}}{B}\right) \]

      8. remove-double-neg 62.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}\right)}{B}\right) \]

      9. +-commutative 62.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)}{B}\right) \]

      10. unpow2 62.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)}{B}\right) \]

      11. unpow2 62.1%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \]

      12. hypot-def 81.5%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)}{B}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around -inf 55.8%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 55.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right) \]

      2. unsub-neg 55.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   6. Simplified 55.8%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right) \]

   7. Taylor expanded in C around 0 49.9%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{B - A}{B}\right)} \]

   if 1.5e-72 < C

   1. Initial program 22.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 22.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. unpow2 22.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 22.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right) \cdot \frac{1}{B}\right)}}{\pi} \]

      2. associate--l- 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)} \cdot \frac{1}{B}\right)}{\pi} \]

      3. +-commutative 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{B \cdot B + {\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      4. unpow2 20.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      5. hypot-udef 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\left(C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}{\pi} \]

      6. div-inv 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}}{\pi} \]

      7. clear-num 58.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   5. Applied egg-rr 58.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 24.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. unpow2 24.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 24.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 59.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   8. Simplified 59.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   9. Taylor expanded in C around inf 63.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   10. Taylor expanded in B around 0 63.9%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 24: 45.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.45e-183)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7e-105)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.45e-183) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7e-105) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.45e-183) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7e-105) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.45e-183:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7e-105:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.45e-183)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7e-105)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.45e-183)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7e-105)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.45e-183], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-105], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.45e-183

   1. Initial program 54.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 51.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.45e-183 < B < 7e-105

   1. Initial program 48.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 48.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 48.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 48.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 48.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 48.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in C around inf 48.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. distribute-rgt1-in 48.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 48.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 48.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 48.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 48.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 7e-105 < B

   1. Initial program 57.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 57.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 82.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 59.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 25: 40.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.999999999999969e-311

   1. Initial program 53.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 53.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 53.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 53.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 53.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 79.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 42.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -9.999999999999969e-311 < B

   1. Initial program 54.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 54.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 54.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 54.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 54.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 83.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 44.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 26: 21.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.9%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Step-by-step derivation

   1. associate-*l/ 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

   2. *-lft-identity 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

   3. +-commutative 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

   4. unpow2 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

   5. unpow2 53.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

   6. hypot-def 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 22.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

5. Final simplification 22.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023257 
(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)))