ABCF->ab-angle angle

Percentage Accurate: 53.1% → 88.9%

Time: 15.8s

Alternatives: 18

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: 53.1% 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: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5 \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \end{array} \end{array} \]

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 -0.5) (not (<= t_0 0.0)))
     (* (atan (/ (- (- C A) (hypot B (- C A))) B)) (/ 180.0 PI))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))))

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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	}
	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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	}
	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 <= -0.5) or not (t_0 <= 0.0):
		tmp = math.atan((((C - A) - math.hypot(B, (C - A))) / B)) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	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 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	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 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	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, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $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))))) < -0.5 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 56.6%

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

      1. associate-*r/ 56.6%

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

      2. associate-*l/ 56.6%

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

      3. *-commutative 56.6%

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

   3. Simplified 85.6%

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

   if -0.5 < (*.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 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-commutative 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in B around 0 99.5%

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

      1. associate-*r/ 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5 \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \end{array} \]

Alternative 2: 72.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.3e-161)
   (/ (* 180.0 (atan (/ (* B 0.5) (- A C)))) PI)
   (if (<= A 8e+57)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e-161) {
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / ((double) M_PI);
	} else if (A <= 8e+57) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e-161) {
		tmp = (180.0 * Math.atan(((B * 0.5) / (A - C)))) / Math.PI;
	} else if (A <= 8e+57) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.3e-161:
		tmp = (180.0 * math.atan(((B * 0.5) / (A - C)))) / math.pi
	elif A <= 8e+57:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.3e-161)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / Float64(A - C)))) / pi);
	elseif (A <= 8e+57)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.3e-161)
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / pi;
	elseif (A <= 8e+57)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.3e-161], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 8e+57], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.3e-161

   1. Initial program 30.2%

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

      1. associate-*r/ 30.2%

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

      2. associate-*l/ 30.2%

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

      3. *-commutative 30.2%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in B around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in C around -inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. sub-neg 68.4%

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

   9. Simplified 68.4%

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

       1. associate-*r/ 68.6%

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

       2. associate-*r/ 68.6%

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

   11. Applied egg-rr 68.6%

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

   if -2.3e-161 < A < 8.00000000000000039e57

   1. Initial program 52.1%

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

      1. associate-*r/ 52.1%

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

      2. associate-*l/ 52.1%

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

      3. associate-*l/ 52.1%

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

      4. *-lft-identity 52.1%

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

      5. sub-neg 52.1%

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

      6. associate-+l- 52.1%

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

      7. sub-neg 52.1%

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

      8. remove-double-neg 52.1%

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

      9. +-commutative 52.1%

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

      10. unpow2 52.1%

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

      11. unpow2 52.1%

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

      12. hypot-def 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around 0 46.9%

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

      1. unpow2 46.9%

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

      2. unpow2 46.9%

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

      3. hypot-def 76.1%

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

   6. Simplified 76.1%

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

   if 8.00000000000000039e57 < A

   1. Initial program 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*l/ 83.3%

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

      3. *-commutative 83.3%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in B around -inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. div-sub 91.2%

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

   6. Simplified 91.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]

Alternative 3: 52.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3.15 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B C)))))
        (t_1 (* (/ 180.0 PI) (atan (* 0.5 (/ B A)))))
        (t_2 (* (/ 180.0 PI) (atan (/ (+ B C) B)))))
   (if (<= A -1.05e-41)
     t_1
     (if (<= A -2.9e-173)
       t_0
       (if (<= A -8.6e-174)
         t_1
         (if (<= A 3.15e-289)
           t_2
           (if (<= A 1.25e-160)
             t_0
             (if (<= A 2.3e-139)
               t_2
               (if (<= A 2.1e-79)
                 t_0
                 (if (<= A 1.08e+130)
                   t_2
                   (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))))))))))

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((0.5 * (B / A)));
	double t_2 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double tmp;
	if (A <= -1.05e-41) {
		tmp = t_1;
	} else if (A <= -2.9e-173) {
		tmp = t_0;
	} else if (A <= -8.6e-174) {
		tmp = t_1;
	} else if (A <= 3.15e-289) {
		tmp = t_2;
	} else if (A <= 1.25e-160) {
		tmp = t_0;
	} else if (A <= 2.3e-139) {
		tmp = t_2;
	} else if (A <= 2.1e-79) {
		tmp = t_0;
	} else if (A <= 1.08e+130) {
		tmp = t_2;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	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((0.5 * (B / A)));
	double t_2 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double tmp;
	if (A <= -1.05e-41) {
		tmp = t_1;
	} else if (A <= -2.9e-173) {
		tmp = t_0;
	} else if (A <= -8.6e-174) {
		tmp = t_1;
	} else if (A <= 3.15e-289) {
		tmp = t_2;
	} else if (A <= 1.25e-160) {
		tmp = t_0;
	} else if (A <= 2.3e-139) {
		tmp = t_2;
	} else if (A <= 2.1e-79) {
		tmp = t_0;
	} else if (A <= 1.08e+130) {
		tmp = t_2;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	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((0.5 * (B / A)))
	t_2 = (180.0 / math.pi) * math.atan(((B + C) / B))
	tmp = 0
	if A <= -1.05e-41:
		tmp = t_1
	elif A <= -2.9e-173:
		tmp = t_0
	elif A <= -8.6e-174:
		tmp = t_1
	elif A <= 3.15e-289:
		tmp = t_2
	elif A <= 1.25e-160:
		tmp = t_0
	elif A <= 2.3e-139:
		tmp = t_2
	elif A <= 2.1e-79:
		tmp = t_0
	elif A <= 1.08e+130:
		tmp = t_2
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))))
	t_2 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)))
	tmp = 0.0
	if (A <= -1.05e-41)
		tmp = t_1;
	elseif (A <= -2.9e-173)
		tmp = t_0;
	elseif (A <= -8.6e-174)
		tmp = t_1;
	elseif (A <= 3.15e-289)
		tmp = t_2;
	elseif (A <= 1.25e-160)
		tmp = t_0;
	elseif (A <= 2.3e-139)
		tmp = t_2;
	elseif (A <= 2.1e-79)
		tmp = t_0;
	elseif (A <= 1.08e+130)
		tmp = t_2;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	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((0.5 * (B / A)));
	t_2 = (180.0 / pi) * atan(((B + C) / B));
	tmp = 0.0;
	if (A <= -1.05e-41)
		tmp = t_1;
	elseif (A <= -2.9e-173)
		tmp = t_0;
	elseif (A <= -8.6e-174)
		tmp = t_1;
	elseif (A <= 3.15e-289)
		tmp = t_2;
	elseif (A <= 1.25e-160)
		tmp = t_0;
	elseif (A <= 2.3e-139)
		tmp = t_2;
	elseif (A <= 2.1e-79)
		tmp = t_0;
	elseif (A <= 1.08e+130)
		tmp = t_2;
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.05e-41], t$95$1, If[LessEqual[A, -2.9e-173], t$95$0, If[LessEqual[A, -8.6e-174], t$95$1, If[LessEqual[A, 3.15e-289], t$95$2, If[LessEqual[A, 1.25e-160], t$95$0, If[LessEqual[A, 2.3e-139], t$95$2, If[LessEqual[A, 2.1e-79], t$95$0, If[LessEqual[A, 1.08e+130], t$95$2, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.05000000000000006e-41 or -2.8999999999999998e-173 < A < -8.6000000000000006e-174

   1. Initial program 29.1%

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

      1. associate-*r/ 29.1%

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

      2. associate-*l/ 29.1%

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

      3. *-commutative 29.1%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in A around -inf 63.7%

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

   if -1.05000000000000006e-41 < A < -2.8999999999999998e-173 or 3.1500000000000001e-289 < A < 1.24999999999999999e-160 or 2.30000000000000012e-139 < A < 2.0999999999999999e-79

   1. Initial program 37.1%

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

      1. associate-*r/ 37.0%

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

      2. associate-*l/ 37.1%

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

      3. *-commutative 37.1%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in B around 0 32.6%

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

      1. unpow2 32.6%

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

   6. Simplified 32.6%

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

   7. Taylor expanded in C around inf 47.7%

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

   if -8.6000000000000006e-174 < A < 3.1500000000000001e-289 or 1.24999999999999999e-160 < A < 2.30000000000000012e-139 or 2.0999999999999999e-79 < A < 1.08e130

   1. Initial program 62.5%

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

      1. associate-*r/ 62.5%

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

      2. associate-*l/ 62.5%

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

      3. associate-*l/ 62.5%

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

      4. *-lft-identity 62.5%

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

      5. sub-neg 62.5%

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

      6. associate-+l- 62.5%

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

      7. sub-neg 62.5%

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

      8. remove-double-neg 62.5%

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

      9. +-commutative 62.5%

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

      10. unpow2 62.5%

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

      11. unpow2 62.5%

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

      12. hypot-def 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in A around 0 55.0%

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

      1. unpow2 55.0%

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

      2. unpow2 55.0%

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

      3. hypot-def 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in B around -inf 62.3%

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

   if 1.08e130 < A

   1. Initial program 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*l/ 89.2%

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

      3. *-commutative 89.2%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in A around inf 88.0%

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

      1. *-commutative 88.0%

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

   6. Simplified 88.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-173}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 3.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-160}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-139}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 4: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{if}\;A \leq -7 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.2 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{-139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-53}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (+ B C) B))))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B (- A C)))) PI))))
   (if (<= A -7e-176)
     t_1
     (if (<= A 1.45e-281)
       t_0
       (if (<= A 8.2e-200)
         t_1
         (if (<= A 2.45e-139)
           t_0
           (if (<= A 1.5e-78)
             (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
             (if (<= A 5.2e-53)
               t_0
               (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double t_1 = 180.0 * (atan((0.5 * (B / (A - C)))) / ((double) M_PI));
	double tmp;
	if (A <= -7e-176) {
		tmp = t_1;
	} else if (A <= 1.45e-281) {
		tmp = t_0;
	} else if (A <= 8.2e-200) {
		tmp = t_1;
	} else if (A <= 2.45e-139) {
		tmp = t_0;
	} else if (A <= 1.5e-78) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (A <= 5.2e-53) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double t_1 = 180.0 * (Math.atan((0.5 * (B / (A - C)))) / Math.PI);
	double tmp;
	if (A <= -7e-176) {
		tmp = t_1;
	} else if (A <= 1.45e-281) {
		tmp = t_0;
	} else if (A <= 8.2e-200) {
		tmp = t_1;
	} else if (A <= 2.45e-139) {
		tmp = t_0;
	} else if (A <= 1.5e-78) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (A <= 5.2e-53) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B + C) / B))
	t_1 = 180.0 * (math.atan((0.5 * (B / (A - C)))) / math.pi)
	tmp = 0
	if A <= -7e-176:
		tmp = t_1
	elif A <= 1.45e-281:
		tmp = t_0
	elif A <= 8.2e-200:
		tmp = t_1
	elif A <= 2.45e-139:
		tmp = t_0
	elif A <= 1.5e-78:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif A <= 5.2e-53:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / Float64(A - C)))) / pi))
	tmp = 0.0
	if (A <= -7e-176)
		tmp = t_1;
	elseif (A <= 1.45e-281)
		tmp = t_0;
	elseif (A <= 8.2e-200)
		tmp = t_1;
	elseif (A <= 2.45e-139)
		tmp = t_0;
	elseif (A <= 1.5e-78)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (A <= 5.2e-53)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B + C) / B));
	t_1 = 180.0 * (atan((0.5 * (B / (A - C)))) / pi);
	tmp = 0.0;
	if (A <= -7e-176)
		tmp = t_1;
	elseif (A <= 1.45e-281)
		tmp = t_0;
	elseif (A <= 8.2e-200)
		tmp = t_1;
	elseif (A <= 2.45e-139)
		tmp = t_0;
	elseif (A <= 1.5e-78)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (A <= 5.2e-53)
		tmp = t_0;
	else
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7e-176], t$95$1, If[LessEqual[A, 1.45e-281], t$95$0, If[LessEqual[A, 8.2e-200], t$95$1, If[LessEqual[A, 2.45e-139], t$95$0, If[LessEqual[A, 1.5e-78], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.2e-53], t$95$0, N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7e-176 or 1.44999999999999995e-281 < A < 8.19999999999999974e-200

   1. Initial program 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-*l/ 30.6%

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

      3. *-commutative 30.6%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around 0 43.9%

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

      1. unpow2 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in C around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. sub-neg 65.3%

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

   9. Simplified 65.3%

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

   if -7e-176 < A < 1.44999999999999995e-281 or 8.19999999999999974e-200 < A < 2.45000000000000016e-139 or 1.49999999999999994e-78 < A < 5.19999999999999993e-53

   1. Initial program 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.3%

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

      3. associate-*l/ 59.3%

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

      4. *-lft-identity 59.3%

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

      5. sub-neg 59.3%

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

      6. associate-+l- 59.3%

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

      7. sub-neg 59.3%

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

      8. remove-double-neg 59.3%

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

      9. +-commutative 59.3%

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

      10. unpow2 59.3%

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

      11. unpow2 59.3%

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

      12. hypot-def 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in A around 0 57.4%

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

      1. unpow2 57.4%

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

      2. unpow2 57.4%

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

      3. hypot-def 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in B around -inf 61.5%

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

   if 2.45000000000000016e-139 < A < 1.49999999999999994e-78

   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. associate-*l/ 43.5%

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

      3. *-commutative 43.5%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in B around 0 41.2%

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

      1. unpow2 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in C around inf 52.8%

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

   if 5.19999999999999993e-53 < A

   1. Initial program 77.7%

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

      1. associate-*r/ 77.7%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in B around -inf 80.6%

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

      1. associate--l+ 80.6%

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

      2. div-sub 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in C around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in A around 0 83.5%

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

       1. associate-*r/ 83.5%

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

       2. mul-1-neg 83.5%

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

       3. sub-neg 83.5%

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

   12. Simplified 83.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-281}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 8.2 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{-139}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 55.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-188}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+156}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{+185}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{-1}{C}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)))
   (if (<= C -4.8e-29)
     (* (/ 180.0 PI) (atan (/ (+ B C) B)))
     (if (<= C 9.5e-188)
       t_0
       (if (<= C 2.5e-112)
         (* (/ 180.0 PI) (atan -1.0))
         (if (<= C 4.7e+156)
           (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
           (if (<= C 1.05e+185)
             t_0
             (* 180.0 (/ (atan (* 0.5 (* B (/ -1.0 C)))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	double tmp;
	if (C <= -4.8e-29) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (C <= 9.5e-188) {
		tmp = t_0;
	} else if (C <= 2.5e-112) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else if (C <= 4.7e+156) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (C <= 1.05e+185) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((0.5 * (B * (-1.0 / C)))) / ((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 - (A / B)))) / Math.PI;
	double tmp;
	if (C <= -4.8e-29) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (C <= 9.5e-188) {
		tmp = t_0;
	} else if (C <= 2.5e-112) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else if (C <= 4.7e+156) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (C <= 1.05e+185) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((0.5 * (B * (-1.0 / C)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	tmp = 0
	if C <= -4.8e-29:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif C <= 9.5e-188:
		tmp = t_0
	elif C <= 2.5e-112:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	elif C <= 4.7e+156:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif C <= 1.05e+185:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((0.5 * (B * (-1.0 / C)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi)
	tmp = 0.0
	if (C <= -4.8e-29)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (C <= 9.5e-188)
		tmp = t_0;
	elseif (C <= 2.5e-112)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	elseif (C <= 4.7e+156)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (C <= 1.05e+185)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B * Float64(-1.0 / C)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((1.0 - (A / B)))) / pi;
	tmp = 0.0;
	if (C <= -4.8e-29)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (C <= 9.5e-188)
		tmp = t_0;
	elseif (C <= 2.5e-112)
		tmp = (180.0 / pi) * atan(-1.0);
	elseif (C <= 4.7e+156)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (C <= 1.05e+185)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((0.5 * (B * (-1.0 / C)))) / 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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -4.8e-29], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.5e-188], t$95$0, If[LessEqual[C, 2.5e-112], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.7e+156], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.05e+185], t$95$0, N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B * N[(-1.0 / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -4.79999999999999984e-29

   1. Initial program 72.0%

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

      1. associate-*r/ 72.0%

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

      2. associate-*l/ 72.0%

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

      3. associate-*l/ 72.0%

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

      4. *-lft-identity 72.0%

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

      5. sub-neg 72.0%

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

      6. associate-+l- 70.5%

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

      7. sub-neg 70.5%

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

      8. remove-double-neg 70.5%

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

      9. +-commutative 70.5%

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

      10. unpow2 70.5%

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

      11. unpow2 70.5%

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

      12. hypot-def 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in A around 0 69.6%

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

      1. unpow2 69.6%

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

      2. unpow2 69.6%

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

      3. hypot-def 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in B around -inf 73.9%

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

   if -4.79999999999999984e-29 < C < 9.50000000000000063e-188 or 4.7e156 < C < 1.05e185

   1. Initial program 52.1%

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

      1. associate-*r/ 52.1%

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

      2. associate-*l/ 52.1%

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

      3. *-commutative 52.1%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in B around -inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. div-sub 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in C around 0 52.2%

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

      1. neg-mul-1 52.2%

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

      2. distribute-neg-frac 52.2%

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

   9. Simplified 52.2%

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

   10. Taylor expanded in A around 0 52.2%

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

       1. associate-*r/ 52.2%

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

       2. mul-1-neg 52.2%

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

       3. sub-neg 52.2%

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

   12. Simplified 52.2%

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

   if 9.50000000000000063e-188 < C < 2.50000000000000022e-112

   1. Initial program 25.5%

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

      1. associate-*r/ 25.5%

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

      2. associate-*l/ 25.5%

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

      3. *-commutative 25.5%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in B around inf 54.8%

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

   if 2.50000000000000022e-112 < C < 4.7e156

   1. Initial program 49.6%

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

      1. associate-*r/ 49.6%

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

      2. associate-*l/ 49.6%

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

      3. *-commutative 49.6%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in B around 0 32.4%

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

      1. unpow2 32.4%

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

   6. Simplified 32.4%

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

   7. Taylor expanded in C around inf 55.1%

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

   if 1.05e185 < C

   1. Initial program 9.5%

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

      1. associate-*r/ 9.5%

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

      2. associate-*l/ 9.5%

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

      3. *-commutative 9.5%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in B around 0 65.0%

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

      1. unpow2 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in C around -inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. sub-neg 86.2%

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

   9. Simplified 86.2%

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

       1. div-inv 86.3%

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

   11. Applied egg-rr 86.3%

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

   12. Taylor expanded in A around 0 85.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+156}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{+185}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{-1}{C}\right)\right)}{\pi}\\ \end{array} \]

Alternative 6: 55.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-188}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 1.62 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+156} \lor \neg \left(C \leq 1.05 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)))
   (if (<= C -1.45e-28)
     (* (/ 180.0 PI) (atan (/ (+ B C) B)))
     (if (<= C 9.5e-188)
       t_0
       (if (<= C 1.62e-112)
         (* (/ 180.0 PI) (atan -1.0))
         (if (or (<= C 4.7e+156) (not (<= C 1.05e+185)))
           (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
           t_0))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	double tmp;
	if (C <= -1.45e-28) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (C <= 9.5e-188) {
		tmp = t_0;
	} else if (C <= 1.62e-112) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else if ((C <= 4.7e+156) || !(C <= 1.05e+185)) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	double tmp;
	if (C <= -1.45e-28) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (C <= 9.5e-188) {
		tmp = t_0;
	} else if (C <= 1.62e-112) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else if ((C <= 4.7e+156) || !(C <= 1.05e+185)) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	tmp = 0
	if C <= -1.45e-28:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif C <= 9.5e-188:
		tmp = t_0
	elif C <= 1.62e-112:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	elif (C <= 4.7e+156) or not (C <= 1.05e+185):
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi)
	tmp = 0.0
	if (C <= -1.45e-28)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (C <= 9.5e-188)
		tmp = t_0;
	elseif (C <= 1.62e-112)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	elseif ((C <= 4.7e+156) || !(C <= 1.05e+185))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((1.0 - (A / B)))) / pi;
	tmp = 0.0;
	if (C <= -1.45e-28)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (C <= 9.5e-188)
		tmp = t_0;
	elseif (C <= 1.62e-112)
		tmp = (180.0 / pi) * atan(-1.0);
	elseif ((C <= 4.7e+156) || ~((C <= 1.05e+185)))
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -1.45e-28], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.5e-188], t$95$0, If[LessEqual[C, 1.62e-112], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 4.7e+156], N[Not[LessEqual[C, 1.05e+185]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.45000000000000006e-28

   1. Initial program 72.0%

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

      1. associate-*r/ 72.0%

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

      2. associate-*l/ 72.0%

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

      3. associate-*l/ 72.0%

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

      4. *-lft-identity 72.0%

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

      5. sub-neg 72.0%

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

      6. associate-+l- 70.5%

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

      7. sub-neg 70.5%

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

      8. remove-double-neg 70.5%

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

      9. +-commutative 70.5%

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

      10. unpow2 70.5%

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

      11. unpow2 70.5%

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

      12. hypot-def 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in A around 0 69.6%

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

      1. unpow2 69.6%

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

      2. unpow2 69.6%

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

      3. hypot-def 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in B around -inf 73.9%

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

   if -1.45000000000000006e-28 < C < 9.50000000000000063e-188 or 4.7e156 < C < 1.05e185

   1. Initial program 52.1%

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

      1. associate-*r/ 52.1%

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

      2. associate-*l/ 52.1%

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

      3. *-commutative 52.1%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in B around -inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. div-sub 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in C around 0 52.2%

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

      1. neg-mul-1 52.2%

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

      2. distribute-neg-frac 52.2%

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

   9. Simplified 52.2%

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

   10. Taylor expanded in A around 0 52.2%

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

       1. associate-*r/ 52.2%

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

       2. mul-1-neg 52.2%

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

       3. sub-neg 52.2%

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

   12. Simplified 52.2%

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

   if 9.50000000000000063e-188 < C < 1.62000000000000009e-112

   1. Initial program 25.5%

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

      1. associate-*r/ 25.5%

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

      2. associate-*l/ 25.5%

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

      3. *-commutative 25.5%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in B around inf 54.8%

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

   if 1.62000000000000009e-112 < C < 4.7e156 or 1.05e185 < C

   1. Initial program 36.2%

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

      1. associate-*r/ 36.2%

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

      2. associate-*l/ 36.2%

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

      3. *-commutative 36.2%

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

   3. Simplified 57.6%

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

   4. Taylor expanded in B around 0 43.3%

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

      1. unpow2 43.3%

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

   6. Simplified 43.3%

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

   7. Taylor expanded in C around inf 65.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.62 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{+156} \lor \neg \left(C \leq 1.05 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 49.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;C \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq 6.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-156}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B C)))))
   (if (<= C -2.05e-54)
     (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
     (if (<= C 6.7e-217)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= C 2.4e-189)
         (* 180.0 (/ t_0 PI))
         (if (<= C 7e-156)
           (* (/ 180.0 PI) (atan -1.0))
           (if (<= C 4.7e-132)
             (* (/ 180.0 PI) (atan 1.0))
             (* (/ 180.0 PI) t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / C)));
	double tmp;
	if (C <= -2.05e-54) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else if (C <= 6.7e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 2.4e-189) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (C <= 7e-156) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else if (C <= 4.7e-132) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / C)));
	double tmp;
	if (C <= -2.05e-54) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else if (C <= 6.7e-217) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 2.4e-189) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (C <= 7e-156) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else if (C <= 4.7e-132) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / C)))
	tmp = 0
	if C <= -2.05e-54:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	elif C <= 6.7e-217:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 2.4e-189:
		tmp = 180.0 * (t_0 / math.pi)
	elif C <= 7e-156:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	elif C <= 4.7e-132:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / C)))
	tmp = 0.0
	if (C <= -2.05e-54)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	elseif (C <= 6.7e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 2.4e-189)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (C <= 7e-156)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	elseif (C <= 4.7e-132)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (C <= -2.05e-54)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	elseif (C <= 6.7e-217)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 2.4e-189)
		tmp = 180.0 * (t_0 / pi);
	elseif (C <= 7e-156)
		tmp = (180.0 / pi) * atan(-1.0);
	elseif (C <= 4.7e-132)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[C, -2.05e-54], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.7e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.4e-189], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7e-156], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.7e-132], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if C < -2.05e-54

   1. Initial program 70.7%

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

      1. associate-*r/ 70.7%

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

      2. associate-*l/ 70.7%

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

      3. *-commutative 70.7%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in C around -inf 62.4%

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

   if -2.05e-54 < C < 6.7000000000000001e-217

   1. Initial program 47.9%

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

      1. associate-*r/ 47.9%

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

      2. associate-*l/ 47.9%

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

      3. *-commutative 47.9%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in A around -inf 38.8%

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

   if 6.7000000000000001e-217 < C < 2.3999999999999998e-189

   1. Initial program 66.4%

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

      1. associate-*r/ 66.4%

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

      2. associate-*l/ 66.4%

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

      3. *-commutative 66.4%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in B around 0 7.5%

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

      1. unpow2 7.5%

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

   6. Simplified 7.5%

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

   7. Taylor expanded in C around -inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. sub-neg 33.0%

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

   9. Simplified 33.0%

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

   10. Taylor expanded in A around 0 50.0%

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

   if 2.3999999999999998e-189 < C < 6.9999999999999999e-156

   1. Initial program 43.2%

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

      1. associate-*r/ 43.2%

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

      2. associate-*l/ 43.2%

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

      3. *-commutative 43.2%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in B around inf 54.1%

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

   if 6.9999999999999999e-156 < C < 4.7000000000000002e-132

   1. Initial program 18.8%

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

      1. associate-*r/ 18.8%

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

      2. associate-*l/ 18.8%

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

      3. *-commutative 18.8%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around -inf 60.6%

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

   if 4.7000000000000002e-132 < C

   1. Initial program 37.3%

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

      1. associate-*r/ 37.3%

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

      2. associate-*l/ 37.3%

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

      3. *-commutative 37.3%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in B around 0 40.4%

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

      1. unpow2 40.4%

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

   6. Simplified 40.4%

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

   7. Taylor expanded in C around inf 60.0%

      \[\leadsto \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq 6.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-156}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 8: 46.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{+61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))))
   (if (<= B -3.1e+61)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= B 1.3e-256)
       t_0
       (if (<= B 1.65e-61)
         (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
         (if (<= B 2.6e+21) t_0 (* (/ 180.0 PI) (atan -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	double tmp;
	if (B <= -3.1e+61) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.3e-256) {
		tmp = t_0;
	} else if (B <= 1.65e-61) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 2.6e+21) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	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 / A)));
	double tmp;
	if (B <= -3.1e+61) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.3e-256) {
		tmp = t_0;
	} else if (B <= 1.65e-61) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 2.6e+21) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	tmp = 0
	if B <= -3.1e+61:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.3e-256:
		tmp = t_0
	elif B <= 1.65e-61:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 2.6e+21:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))))
	tmp = 0.0
	if (B <= -3.1e+61)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.3e-256)
		tmp = t_0;
	elseif (B <= 1.65e-61)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 2.6e+21)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((0.5 * (B / A)));
	tmp = 0.0;
	if (B <= -3.1e+61)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.3e-256)
		tmp = t_0;
	elseif (B <= 1.65e-61)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 2.6e+21)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.1e+61], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-256], t$95$0, If[LessEqual[B, 1.65e-61], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e+21], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.0999999999999999e61

   1. Initial program 49.8%

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

      1. associate-*r/ 49.8%

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

      2. associate-*l/ 49.8%

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

      3. *-commutative 49.8%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in B around -inf 64.2%

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

   if -3.0999999999999999e61 < B < 1.3e-256 or 1.64999999999999998e-61 < B < 2.6e21

   1. Initial program 57.2%

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

      1. associate-*r/ 57.2%

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

      2. associate-*l/ 57.2%

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

      3. *-commutative 57.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in A around -inf 38.8%

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

   if 1.3e-256 < B < 1.64999999999999998e-61

   1. Initial program 43.8%

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

      1. associate-*r/ 43.8%

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

      2. associate-*l/ 43.8%

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

      3. *-commutative 43.8%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in B around 0 41.9%

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

      1. unpow2 41.9%

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

   6. Simplified 41.9%

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

   7. Taylor expanded in C around inf 50.6%

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

   if 2.6e21 < B

   1. Initial program 46.0%

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

      1. associate-*r/ 46.0%

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

      2. associate-*l/ 46.0%

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

      3. *-commutative 46.0%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in B around inf 69.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{+61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-256}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 9: 49.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -9.6 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))))
   (if (<= A -2.8e-41)
     (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
     (if (<= A -9.6e-244)
       t_0
       (if (<= A 3.5e-301)
         (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
         (if (<= A 6e-47) t_0 (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	double tmp;
	if (A <= -2.8e-41) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= -9.6e-244) {
		tmp = t_0;
	} else if (A <= 3.5e-301) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else if (A <= 6e-47) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	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 tmp;
	if (A <= -2.8e-41) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= -9.6e-244) {
		tmp = t_0;
	} else if (A <= 3.5e-301) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else if (A <= 6e-47) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	tmp = 0
	if A <= -2.8e-41:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= -9.6e-244:
		tmp = t_0
	elif A <= 3.5e-301:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	elif A <= 6e-47:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))))
	tmp = 0.0
	if (A <= -2.8e-41)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= -9.6e-244)
		tmp = t_0;
	elseif (A <= 3.5e-301)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	elseif (A <= 6e-47)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (A <= -2.8e-41)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= -9.6e-244)
		tmp = t_0;
	elseif (A <= 3.5e-301)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	elseif (A <= 6e-47)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.8e-41], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9.6e-244], t$95$0, If[LessEqual[A, 3.5e-301], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-47], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.8000000000000002e-41

   1. Initial program 29.4%

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

      1. associate-*r/ 29.4%

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

      2. associate-*l/ 29.4%

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

      3. *-commutative 29.4%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in A around -inf 63.2%

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

   if -2.8000000000000002e-41 < A < -9.60000000000000063e-244 or 3.49999999999999992e-301 < A < 6.00000000000000033e-47

   1. Initial program 40.0%

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

      1. associate-*r/ 40.0%

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

      2. associate-*l/ 40.0%

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

      3. *-commutative 40.0%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in B around 0 27.6%

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

      1. unpow2 27.6%

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

   6. Simplified 27.6%

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

   7. Taylor expanded in C around inf 40.4%

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

   if -9.60000000000000063e-244 < A < 3.49999999999999992e-301

   1. Initial program 73.4%

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

      1. associate-*r/ 73.4%

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

      2. associate-*l/ 73.4%

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

      3. *-commutative 73.4%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in C around -inf 43.9%

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

   if 6.00000000000000033e-47 < A

   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-*r/ 79.3%

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

      2. associate-*l/ 79.3%

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

      3. *-commutative 79.3%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in A around inf 72.0%

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

      1. *-commutative 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -9.6 \cdot 10^{-244}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-47}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 10: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{if}\;A \leq -8.2 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-282}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-199}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 0.5 (/ B (- A C)))) PI))))
   (if (<= A -8.2e-174)
     t_0
     (if (<= A 2.1e-282)
       (* (/ 180.0 PI) (atan (/ (+ B C) B)))
       (if (<= A 5.9e-199)
         t_0
         (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.5 * (B / (A - C)))) / ((double) M_PI));
	double tmp;
	if (A <= -8.2e-174) {
		tmp = t_0;
	} else if (A <= 2.1e-282) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (A <= 5.9e-199) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.5 * (B / (A - C)))) / Math.PI);
	double tmp;
	if (A <= -8.2e-174) {
		tmp = t_0;
	} else if (A <= 2.1e-282) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (A <= 5.9e-199) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.5 * (B / (A - C)))) / math.pi)
	tmp = 0
	if A <= -8.2e-174:
		tmp = t_0
	elif A <= 2.1e-282:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif A <= 5.9e-199:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / Float64(A - C)))) / pi))
	tmp = 0.0
	if (A <= -8.2e-174)
		tmp = t_0;
	elseif (A <= 2.1e-282)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (A <= 5.9e-199)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.5 * (B / (A - C)))) / pi);
	tmp = 0.0;
	if (A <= -8.2e-174)
		tmp = t_0;
	elseif (A <= 2.1e-282)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (A <= 5.9e-199)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	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 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -8.2e-174], t$95$0, If[LessEqual[A, 2.1e-282], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.9e-199], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.2000000000000002e-174 or 2.10000000000000012e-282 < A < 5.9000000000000003e-199

   1. Initial program 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-*l/ 30.6%

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

      3. *-commutative 30.6%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around 0 43.9%

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

      1. unpow2 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in C around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. sub-neg 65.3%

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

   9. Simplified 65.3%

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

   if -8.2000000000000002e-174 < A < 2.10000000000000012e-282

   1. Initial program 63.8%

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

      1. associate-*r/ 63.8%

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

      2. associate-*l/ 63.8%

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

      3. associate-*l/ 63.8%

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

      4. *-lft-identity 63.8%

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

      5. sub-neg 63.8%

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

      6. associate-+l- 63.8%

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

      7. sub-neg 63.8%

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

      8. remove-double-neg 63.8%

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

      9. +-commutative 63.8%

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

      10. unpow2 63.8%

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

      11. unpow2 63.8%

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

      12. hypot-def 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in A around 0 63.8%

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

      1. unpow2 63.8%

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

      2. unpow2 63.8%

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

      3. hypot-def 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in B around -inf 62.5%

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

   if 5.9000000000000003e-199 < A

   1. Initial program 69.6%

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

      1. associate-*r/ 69.6%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-282}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]

Alternative 11: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -7.5 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-283}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= A -7.5e-175)
     t_0
     (if (<= A 5e-283)
       (* (/ 180.0 PI) (atan (/ (+ B C) B)))
       (if (<= A 3.7e-201)
         t_0
         (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -7.5e-175) {
		tmp = t_0;
	} else if (A <= 5e-283) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (A <= 3.7e-201) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -7.5e-175) {
		tmp = t_0;
	} else if (A <= 5e-283) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (A <= 3.7e-201) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if A <= -7.5e-175:
		tmp = t_0
	elif A <= 5e-283:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif A <= 3.7e-201:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (A <= -7.5e-175)
		tmp = t_0;
	elseif (A <= 5e-283)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (A <= 3.7e-201)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (A <= -7.5e-175)
		tmp = t_0;
	elseif (A <= 5e-283)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (A <= 3.7e-201)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7.5e-175], t$95$0, If[LessEqual[A, 5e-283], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.7e-201], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.50000000000000053e-175 or 5.0000000000000001e-283 < A < 3.6999999999999998e-201

   1. Initial program 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-*l/ 30.6%

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

      3. *-commutative 30.6%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around 0 65.5%

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

      1. associate-*r/ 65.5%

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

   6. Simplified 65.5%

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

   if -7.50000000000000053e-175 < A < 5.0000000000000001e-283

   1. Initial program 63.8%

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

      1. associate-*r/ 63.8%

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

      2. associate-*l/ 63.8%

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

      3. associate-*l/ 63.8%

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

      4. *-lft-identity 63.8%

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

      5. sub-neg 63.8%

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

      6. associate-+l- 63.8%

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

      7. sub-neg 63.8%

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

      8. remove-double-neg 63.8%

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

      9. +-commutative 63.8%

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

      10. unpow2 63.8%

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

      11. unpow2 63.8%

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

      12. hypot-def 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in A around 0 63.8%

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

      1. unpow2 63.8%

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

      2. unpow2 63.8%

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

      3. hypot-def 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in B around -inf 62.5%

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

   if 3.6999999999999998e-201 < A

   1. Initial program 69.6%

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

      1. associate-*r/ 69.6%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-283}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]

Alternative 12: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 2.65 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (* 0.5 (/ B (- A C))))) PI)))
   (if (<= A -3.4e-174)
     t_0
     (if (<= A 1.8e-289)
       (* (/ 180.0 PI) (atan (/ (+ B C) B)))
       (if (<= A 2.65e-201)
         t_0
         (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((0.5 * (B / (A - C))))) / ((double) M_PI);
	double tmp;
	if (A <= -3.4e-174) {
		tmp = t_0;
	} else if (A <= 1.8e-289) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (A <= 2.65e-201) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((0.5 * (B / (A - C))))) / Math.PI;
	double tmp;
	if (A <= -3.4e-174) {
		tmp = t_0;
	} else if (A <= 1.8e-289) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (A <= 2.65e-201) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((0.5 * (B / (A - C))))) / math.pi
	tmp = 0
	if A <= -3.4e-174:
		tmp = t_0
	elif A <= 1.8e-289:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif A <= 2.65e-201:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / Float64(A - C))))) / pi)
	tmp = 0.0
	if (A <= -3.4e-174)
		tmp = t_0;
	elseif (A <= 1.8e-289)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (A <= 2.65e-201)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((0.5 * (B / (A - C))))) / pi;
	tmp = 0.0;
	if (A <= -3.4e-174)
		tmp = t_0;
	elseif (A <= 1.8e-289)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (A <= 2.65e-201)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[A, -3.4e-174], t$95$0, If[LessEqual[A, 1.8e-289], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.65e-201], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.4000000000000002e-174 or 1.8e-289 < A < 2.64999999999999994e-201

   1. Initial program 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-*l/ 30.6%

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

      3. *-commutative 30.6%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around 0 43.9%

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

      1. unpow2 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in C around -inf 65.3%

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

      1. associate-*r/ 65.5%

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

      2. mul-1-neg 65.5%

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

      3. sub-neg 65.5%

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

   9. Simplified 65.5%

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

   if -3.4000000000000002e-174 < A < 1.8e-289

   1. Initial program 63.8%

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

      1. associate-*r/ 63.8%

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

      2. associate-*l/ 63.8%

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

      3. associate-*l/ 63.8%

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

      4. *-lft-identity 63.8%

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

      5. sub-neg 63.8%

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

      6. associate-+l- 63.8%

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

      7. sub-neg 63.8%

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

      8. remove-double-neg 63.8%

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

      9. +-commutative 63.8%

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

      10. unpow2 63.8%

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

      11. unpow2 63.8%

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

      12. hypot-def 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in A around 0 63.8%

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

      1. unpow2 63.8%

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

      2. unpow2 63.8%

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

      3. hypot-def 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in B around -inf 62.5%

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

   if 2.64999999999999994e-201 < A

   1. Initial program 69.6%

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

      1. associate-*r/ 69.6%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 2.65 \cdot 10^{-201}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]

Alternative 13: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-284}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.9e-175)
   (/ (* 180.0 (atan (/ (* B 0.5) (- A C)))) PI)
   (if (<= A 2.3e-284)
     (* (/ 180.0 PI) (atan (/ (+ B C) B)))
     (if (<= A 7.5e-201)
       (/ (* 180.0 (atan (* 0.5 (/ B (- A C))))) PI)
       (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.9e-175) {
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / ((double) M_PI);
	} else if (A <= 2.3e-284) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (A <= 7.5e-201) {
		tmp = (180.0 * atan((0.5 * (B / (A - C))))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.9e-175) {
		tmp = (180.0 * Math.atan(((B * 0.5) / (A - C)))) / Math.PI;
	} else if (A <= 2.3e-284) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (A <= 7.5e-201) {
		tmp = (180.0 * Math.atan((0.5 * (B / (A - C))))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.9e-175:
		tmp = (180.0 * math.atan(((B * 0.5) / (A - C)))) / math.pi
	elif A <= 2.3e-284:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif A <= 7.5e-201:
		tmp = (180.0 * math.atan((0.5 * (B / (A - C))))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.9e-175)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / Float64(A - C)))) / pi);
	elseif (A <= 2.3e-284)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (A <= 7.5e-201)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / Float64(A - C))))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.9e-175)
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / pi;
	elseif (A <= 2.3e-284)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (A <= 7.5e-201)
		tmp = (180.0 * atan((0.5 * (B / (A - C))))) / pi;
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.9e-175], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.3e-284], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.5e-201], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.89999999999999998e-175

   1. Initial program 29.9%

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

      1. associate-*r/ 29.9%

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

      2. associate-*l/ 29.9%

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

      3. *-commutative 29.9%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in B around 0 46.1%

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

      1. unpow2 46.1%

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

   6. Simplified 46.1%

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

   7. Taylor expanded in C around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. sub-neg 68.0%

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

   9. Simplified 68.0%

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

       1. associate-*r/ 68.2%

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

       2. associate-*r/ 68.2%

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

   11. Applied egg-rr 68.2%

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

   if -4.89999999999999998e-175 < A < 2.3e-284

   1. Initial program 63.8%

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

      1. associate-*r/ 63.8%

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

      2. associate-*l/ 63.8%

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

      3. associate-*l/ 63.8%

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

      4. *-lft-identity 63.8%

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

      5. sub-neg 63.8%

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

      6. associate-+l- 63.8%

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

      7. sub-neg 63.8%

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

      8. remove-double-neg 63.8%

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

      9. +-commutative 63.8%

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

      10. unpow2 63.8%

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

      11. unpow2 63.8%

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

      12. hypot-def 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in A around 0 63.8%

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

      1. unpow2 63.8%

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

      2. unpow2 63.8%

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

      3. hypot-def 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in B around -inf 62.5%

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

   if 2.3e-284 < A < 7.49999999999999987e-201

   1. Initial program 34.3%

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

      1. associate-*r/ 34.3%

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

      2. associate-*l/ 34.3%

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

      3. *-commutative 34.3%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in B around 0 32.0%

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

      1. unpow2 32.0%

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

   6. Simplified 32.0%

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

   7. Taylor expanded in C around -inf 51.5%

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

      1. associate-*r/ 51.7%

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

      2. mul-1-neg 51.7%

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

      3. sub-neg 51.7%

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

   9. Simplified 51.7%

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

   if 7.49999999999999987e-201 < A

   1. Initial program 69.6%

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

      1. associate-*r/ 69.6%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{-284}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]

Alternative 14: 46.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.95e+65)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 2.7e-61)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.95e+65) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 2.7e-61) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.95e+65) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 2.7e-61) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.95e+65:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 2.7e-61:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.95e+65)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 2.7e-61)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.95e+65)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 2.7e-61)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.95e+65], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-61], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.9499999999999999e65

   1. Initial program 49.7%

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

      1. associate-*r/ 49.7%

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

      2. associate-*l/ 49.7%

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

      3. *-commutative 49.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in B around -inf 64.9%

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

   if -1.9499999999999999e65 < B < 2.69999999999999993e-61

   1. Initial program 53.4%

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

      1. associate-*r/ 53.4%

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

      2. associate-*l/ 53.4%

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

      3. *-commutative 53.4%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in B around 0 35.8%

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

      1. unpow2 35.8%

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

   6. Simplified 35.8%

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

   7. Taylor expanded in C around -inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. sub-neg 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in A around 0 34.0%

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

   if 2.69999999999999993e-61 < B

   1. Initial program 47.4%

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

      1. associate-*r/ 47.4%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around inf 56.9%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 15: 46.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.85e+65)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 3.2e-61)
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.85e+65) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 3.2e-61) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.85e+65) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 3.2e-61) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.85e+65:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 3.2e-61:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.85e+65)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 3.2e-61)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.85e+65)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 3.2e-61)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.85e+65], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.2e-61], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.84999999999999997e65

   1. Initial program 49.7%

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

      1. associate-*r/ 49.7%

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

      2. associate-*l/ 49.7%

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

      3. *-commutative 49.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in B around -inf 64.9%

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

   if -1.84999999999999997e65 < B < 3.2000000000000001e-61

   1. Initial program 53.4%

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

      1. associate-*r/ 53.4%

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

      2. associate-*l/ 53.4%

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

      3. *-commutative 53.4%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in B around 0 35.8%

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

      1. unpow2 35.8%

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

   6. Simplified 35.8%

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

   7. Taylor expanded in C around inf 34.0%

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

   if 3.2000000000000001e-61 < B

   1. Initial program 47.4%

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

      1. associate-*r/ 47.4%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around inf 56.9%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 16: 44.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.8e-112)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 2.6e-61)
     (* (/ 180.0 PI) (atan 0.0))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.8e-112) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 2.6e-61) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.8e-112) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 2.6e-61) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.8e-112:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 2.6e-61:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.8e-112)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 2.6e-61)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.8e-112)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 2.6e-61)
		tmp = (180.0 / pi) * atan(0.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.8e-112], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-61], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.8000000000000001e-112

   1. Initial program 52.1%

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

      1. associate-*r/ 52.0%

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

      2. associate-*l/ 52.1%

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

      3. *-commutative 52.1%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around -inf 49.7%

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

   if -4.8000000000000001e-112 < B < 2.6000000000000001e-61

   1. Initial program 52.3%

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

      1. associate-*r/ 52.3%

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

      2. associate-*l/ 52.3%

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

      3. associate-*l/ 52.3%

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

      4. *-lft-identity 52.3%

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

      5. sub-neg 52.3%

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

      6. associate-+l- 49.9%

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

      7. sub-neg 49.9%

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

      8. remove-double-neg 49.9%

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

      9. +-commutative 49.9%

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

      10. unpow2 49.9%

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

      11. unpow2 49.9%

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

      12. hypot-def 56.8%

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

   3. Simplified 56.8%

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

      1. div-sub 42.5%

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

   5. Applied egg-rr 42.5%

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

   6. Taylor expanded in C around inf 12.7%

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

      1. distribute-rgt1-in 12.7%

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

      2. metadata-eval 12.7%

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

      3. mul0-lft 26.8%

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

      4. metadata-eval 26.8%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{0} \]

   8. Simplified 26.8%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{0} \]

   if 2.6000000000000001e-61 < B

   1. Initial program 47.4%

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

      1. associate-*r/ 47.4%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around inf 56.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 17: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* (/ 180.0 PI) (atan 1.0)) (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 54.3%

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

      1. associate-*r/ 54.3%

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

      2. associate-*l/ 54.3%

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

      3. *-commutative 54.3%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 37.7%

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

   if -4.999999999999985e-310 < B

   1. Initial program 47.2%

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

      1. associate-*r/ 47.2%

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

      2. associate-*l/ 47.2%

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

      3. *-commutative 47.2%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in B around inf 37.4%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 18: 21.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \frac{180}{\pi} \cdot \tan^{-1} -1 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 50.9%

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

   1. associate-*r/ 50.9%

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

   2. associate-*l/ 50.9%

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

   3. *-commutative 50.9%

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

3. Simplified 75.3%

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

4. Taylor expanded in B around inf 18.9%

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

5. Final simplification 18.9%

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

Reproduce

herbie shell --seed 2023172 
(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)))