ABCF->ab-angle angle

Percentage Accurate: 53.3% → 87.9%

Time: 20.9s

Alternatives: 29

Speedup: 3.5×

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: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-1}{B} \cdot \left(\left(A - C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-9} \lor \neg \left(t\_0 \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \frac{0.5}{A - C}\right)\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ -1.0 B) (+ (- A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -5e-9) (not (<= t_0 4e-5)))
     (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)
     (*
      (atan
       (* B (+ (* 0.125 (/ (pow B 2.0) (pow (- C A) 3.0))) (/ 0.5 (- A C)))))
      (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (-1.0 / B) * ((A - C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-9) || !(t_0 <= 4e-5)) {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	} else {
		tmp = atan((B * ((0.125 * (pow(B, 2.0) / pow((C - A), 3.0))) + (0.5 / (A - C))))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (-1.0 / B) * ((A - C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-9) || !(t_0 <= 4e-5)) {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	} else {
		tmp = Math.atan((B * ((0.125 * (Math.pow(B, 2.0) / Math.pow((C - A), 3.0))) + (0.5 / (A - C))))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-1.0 / B) * ((A - C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -5e-9) or not (t_0 <= 4e-5):
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	else:
		tmp = math.atan((B * ((0.125 * (math.pow(B, 2.0) / math.pow((C - A), 3.0))) + (0.5 / (A - C))))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-1.0 / B) * Float64(Float64(A - C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -5e-9) || !(t_0 <= 4e-5))
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	else
		tmp = Float64(atan(Float64(B * Float64(Float64(0.125 * Float64((B ^ 2.0) / (Float64(C - A) ^ 3.0))) + Float64(0.5 / Float64(A - C))))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (-1.0 / B) * ((A - C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -5e-9) || ~((t_0 <= 4e-5)))
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	else
		tmp = atan((B * ((0.125 * ((B ^ 2.0) / ((C - A) ^ 3.0))) + (0.5 / (A - C))))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-1.0 / B), $MachinePrecision] * N[(N[(A - C), $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, -5e-9], N[Not[LessEqual[t$95$0, 4e-5]], $MachinePrecision]], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(B * N[(N[(0.125 * N[(N[Power[B, 2.0], $MachinePrecision] / N[Power[N[(C - A), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -5.0000000000000001e-9 or 4.00000000000000033e-5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 63.6%

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

      1. associate-*r/ 63.6%

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

      2. associate-*l/ 63.6%

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

      3. *-un-lft-identity 63.6%

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

      4. unpow2 63.6%

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

      5. unpow2 63.6%

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

      6. hypot-define 86.8%

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

   4. Applied egg-rr 86.8%

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

   if -5.0000000000000001e-9 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 4.00000000000000033e-5

   1. Initial program 17.8%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in B around 0 98.7%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - 0.5 \cdot \frac{1}{C - A}\right)\right)} \cdot \frac{180}{\pi} \]
   6. Step-by-step derivation

      1. associate-*r/ 98.7%

         \[\leadsto \tan^{-1} \left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \color{blue}{\frac{0.5 \cdot 1}{C - A}}\right)\right) \cdot \frac{180}{\pi} \]

      2. metadata-eval 98.7%

         \[\leadsto \tan^{-1} \left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{\color{blue}{0.5}}{C - A}\right)\right) \cdot \frac{180}{\pi} \]

   7. Simplified 98.7%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{0.5}{C - A}\right)\right)} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{-1}{B} \cdot \left(\left(A - C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-9} \lor \neg \left(\frac{-1}{B} \cdot \left(\left(A - C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \left(0.125 \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \frac{0.5}{A - C}\right)\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-136}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{C - \mathsf{hypot}\left(B, C\right)}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.9e-8)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (if (<= A 6e-136)
     (/ (* 180.0 (atan (/ 1.0 (/ B (- C (hypot B C)))))) PI)
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B A))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.9e-8) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else if (A <= 6e-136) {
		tmp = (180.0 * atan((1.0 / (B / (C - hypot(B, C)))))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, A))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.9e-8) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else if (A <= 6e-136) {
		tmp = (180.0 * Math.atan((1.0 / (B / (C - Math.hypot(B, C)))))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, A))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.9e-8:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	elif A <= 6e-136:
		tmp = (180.0 * math.atan((1.0 / (B / (C - math.hypot(B, C)))))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, A))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.9e-8)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	elseif (A <= 6e-136)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(B / Float64(C - hypot(B, C)))))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.9e-8)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	elseif (A <= 6e-136)
		tmp = (180.0 * atan((1.0 / (B / (C - hypot(B, C)))))) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, A))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.9e-8], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-136], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(B / N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.89999999999999985e-8

   1. Initial program 23.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in B around 0 80.8%

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

   if -3.89999999999999985e-8 < A < 5.9999999999999996e-136

   1. Initial program 64.0%

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

      1. associate-*r/ 64.0%

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

      2. associate-*l/ 64.0%

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

      3. *-un-lft-identity 64.0%

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

      4. unpow2 64.0%

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

      5. unpow2 64.0%

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

      6. hypot-define 83.3%

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

   4. Applied egg-rr 83.3%

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

      1. clear-num 83.3%

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

      2. associate--l- 83.3%

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

   6. Applied egg-rr 83.3%

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

   7. Taylor expanded in A around 0 63.3%

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

      1. unpow2 63.3%

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

      2. unpow2 63.3%

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

      3. hypot-undefine 82.3%

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

   9. Simplified 82.3%

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

   if 5.9999999999999996e-136 < A

   1. Initial program 73.9%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in C around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. unpow2 73.0%

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

      3. unpow2 73.0%

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

      4. hypot-define 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-136}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{C - \mathsf{hypot}\left(B, C\right)}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.8e-9)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (if (<= A 1.3e-135)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B A))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e-9) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else if (A <= 1.3e-135) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, A))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e-9) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else if (A <= 1.3e-135) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, A))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e-9:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	elif A <= 1.3e-135:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, A))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e-9)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	elseif (A <= 1.3e-135)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e-9)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	elseif (A <= 1.3e-135)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, A))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.8e-9], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.3e-135], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.80000000000000011e-9

   1. Initial program 23.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in B around 0 80.8%

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

   if -3.80000000000000011e-9 < A < 1.30000000000000002e-135

   1. Initial program 64.0%

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

   3. Taylor expanded in A around 0 63.3%

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

      1. unpow2 63.3%

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

      2. unpow2 63.3%

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

      3. hypot-define 82.3%

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

   5. Simplified 82.3%

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

   if 1.30000000000000002e-135 < A

   1. Initial program 73.9%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in C around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. unpow2 73.0%

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

      3. unpow2 73.0%

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

      4. hypot-define 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5.2e+16)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 8.8e-13)
     (/ (* 180.0 (atan (/ (+ A (hypot A B)) (- B)))) PI)
     (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.2e+16) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 8.8e-13) {
		tmp = (180.0 * atan(((A + hypot(A, B)) / -B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.2e+16) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 8.8e-13) {
		tmp = (180.0 * Math.atan(((A + Math.hypot(A, B)) / -B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5.2e+16:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 8.8e-13:
		tmp = (180.0 * math.atan(((A + math.hypot(A, B)) / -B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5.2e+16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 8.8e-13)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(A + hypot(A, B)) / Float64(-B)))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5.2e+16)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 8.8e-13)
		tmp = (180.0 * atan(((A + hypot(A, B)) / -B))) / pi;
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5.2e+16], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.8e-13], N[(N[(180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -5.2e16

   1. Initial program 79.4%

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

   3. Taylor expanded in A around 0 79.4%

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

      1. unpow2 79.4%

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

      2. unpow2 79.4%

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

      3. hypot-define 91.1%

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

   5. Simplified 91.1%

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

   if -5.2e16 < C < 8.79999999999999986e-13

   1. Initial program 64.4%

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

      1. associate-*r/ 64.4%

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

      2. associate-*l/ 64.4%

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

      3. *-un-lft-identity 64.4%

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

      4. unpow2 64.4%

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

      5. unpow2 64.4%

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

      6. hypot-define 83.9%

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

   4. Applied egg-rr 83.9%

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

   5. Taylor expanded in C around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-neg-frac2 61.9%

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

      3. unpow2 61.9%

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

      4. unpow2 61.9%

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

      5. hypot-define 81.5%

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

   7. Simplified 81.5%

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

   if 8.79999999999999986e-13 < C

   1. Initial program 24.8%

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

   3. Simplified 47.3%

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

   5. Taylor expanded in B around 0 75.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5e-10)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (* (/ 180.0 PI) (atan (/ 1.0 (/ B (- C (+ A (hypot B (- C A))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e-10) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 / (B / (C - (A + hypot(B, (C - A)))))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e-10) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 / (B / (C - (A + Math.hypot(B, (C - A)))))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5e-10:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 / (B / (C - (A + math.hypot(B, (C - A)))))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5e-10)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 / Float64(B / Float64(C - Float64(A + hypot(B, Float64(C - A))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5e-10)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	else
		tmp = (180.0 / pi) * atan((1.0 / (B / (C - (A + hypot(B, (C - A)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5e-10], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 / N[(B / N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.00000000000000031e-10

   1. Initial program 23.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in B around 0 80.8%

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

   if -5.00000000000000031e-10 < A

   1. Initial program 68.3%

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

   3. Simplified 87.6%

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

      1. clear-num 87.6%

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

   6. Applied egg-rr 87.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{B}{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e-7)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (if (<= A 9e+132)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-7) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else if (A <= 9e+132) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-7) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else if (A <= 9e+132) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e-7:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	elif A <= 9e+132:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e-7)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	elseif (A <= 9e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e-7)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	elseif (A <= 9e+132)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e-7], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.8999999999999998e-7

   1. Initial program 23.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in B around 0 80.8%

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

   if -2.8999999999999998e-7 < A < 8.99999999999999944e132

   1. Initial program 65.4%

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

   3. Taylor expanded in A around 0 60.3%

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

      1. unpow2 60.3%

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

      2. unpow2 60.3%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in B around inf 85.4%

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

   4. Taylor expanded in C around 0 88.5%

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

      1. neg-mul-1 88.5%

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

      2. distribute-neg-in 88.5%

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

      3. metadata-eval 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e-7)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-7) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-7) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e-7:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e-7)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e-7)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e-7], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.8999999999999998e-7

   1. Initial program 23.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in B around 0 80.8%

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

   if -2.8999999999999998e-7 < A

   1. Initial program 68.3%

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

   3. Simplified 87.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-121} \lor \neg \left(B \leq 3.2 \cdot 10^{-28}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ A (- B))) PI))))
   (if (<= B -2.2e-118)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3.1e-204)
       t_0
       (if (<= B 6.2e-190)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 1.1e-158)
           t_0
           (if (<= B 1.45e-127)
             (/ (* 180.0 (atan (/ B A))) PI)
             (if (or (<= B 2.4e-121) (not (<= B 3.2e-28)))
               (* 180.0 (/ (atan -1.0) PI))
               (* 180.0 (/ (atan (/ C B)) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.2e-118) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.1e-204) {
		tmp = t_0;
	} else if (B <= 6.2e-190) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.1e-158) {
		tmp = t_0;
	} else if (B <= 1.45e-127) {
		tmp = (180.0 * atan((B / A))) / ((double) M_PI);
	} else if ((B <= 2.4e-121) || !(B <= 3.2e-28)) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((A / -B)) / Math.PI);
	double tmp;
	if (B <= -2.2e-118) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.1e-204) {
		tmp = t_0;
	} else if (B <= 6.2e-190) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.1e-158) {
		tmp = t_0;
	} else if (B <= 1.45e-127) {
		tmp = (180.0 * Math.atan((B / A))) / Math.PI;
	} else if ((B <= 2.4e-121) || !(B <= 3.2e-28)) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((A / -B)) / math.pi)
	tmp = 0
	if B <= -2.2e-118:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.1e-204:
		tmp = t_0
	elif B <= 6.2e-190:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.1e-158:
		tmp = t_0
	elif B <= 1.45e-127:
		tmp = (180.0 * math.atan((B / A))) / math.pi
	elif (B <= 2.4e-121) or not (B <= 3.2e-28):
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi))
	tmp = 0.0
	if (B <= -2.2e-118)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.1e-204)
		tmp = t_0;
	elseif (B <= 6.2e-190)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.1e-158)
		tmp = t_0;
	elseif (B <= 1.45e-127)
		tmp = Float64(Float64(180.0 * atan(Float64(B / A))) / pi);
	elseif ((B <= 2.4e-121) || !(B <= 3.2e-28))
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((A / -B)) / pi);
	tmp = 0.0;
	if (B <= -2.2e-118)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.1e-204)
		tmp = t_0;
	elseif (B <= 6.2e-190)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.1e-158)
		tmp = t_0;
	elseif (B <= 1.45e-127)
		tmp = (180.0 * atan((B / A))) / pi;
	elseif ((B <= 2.4e-121) || ~((B <= 3.2e-28)))
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((C / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.2e-118], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.1e-204], t$95$0, If[LessEqual[B, 6.2e-190], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-158], t$95$0, If[LessEqual[B, 1.45e-127], N[(N[(180.0 * N[ArcTan[N[(B / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[Or[LessEqual[B, 2.4e-121], N[Not[LessEqual[B, 3.2e-28]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -2.19999999999999984e-118

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 50.4%

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

   if -2.19999999999999984e-118 < B < -3.0999999999999999e-204 or 6.19999999999999987e-190 < B < 1.1000000000000001e-158

   1. Initial program 75.0%

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

   3. Taylor expanded in B around inf 67.6%

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

   4. Taylor expanded in A around inf 51.6%

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

      1. mul-1-neg 51.6%

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

   6. Simplified 51.6%

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

   if -3.0999999999999999e-204 < B < 6.19999999999999987e-190

   1. Initial program 48.7%

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

   3. Taylor expanded in C around inf 46.2%

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

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. distribute-rgt1-in 46.2%

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

      4. metadata-eval 46.2%

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

      5. mul0-lft 46.2%

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

      6. metadata-eval 46.2%

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

   5. Simplified 46.2%

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

   if 1.1000000000000001e-158 < B < 1.45e-127

   1. Initial program 44.9%

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

      1. associate-*r/ 44.9%

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

      2. associate-*l/ 44.9%

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

      3. *-un-lft-identity 44.9%

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

      4. unpow2 44.9%

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

      5. unpow2 44.9%

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

      6. hypot-define 86.4%

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

   4. Applied egg-rr 86.4%

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

      1. clear-num 86.4%

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

      2. associate--l- 45.1%

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

   6. Applied egg-rr 45.1%

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

   7. Taylor expanded in B around -inf 46.7%

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

      1. associate-*r/ 46.7%

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

      2. mul-1-neg 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in A around inf 74.5%

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

   if 1.45e-127 < B < 2.40000000000000003e-121 or 3.19999999999999982e-28 < B

   1. Initial program 56.4%

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

   3. Taylor expanded in B around inf 61.7%

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

   if 2.40000000000000003e-121 < B < 3.19999999999999982e-28

   1. Initial program 61.5%

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

   3. Taylor expanded in B around inf 54.0%

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

   4. Taylor expanded in C around inf 47.8%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-121} \lor \neg \left(B \leq 3.2 \cdot 10^{-28}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{if}\;A \leq -1.65 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -1.12 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-234}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-1 - \frac{C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))))
   (if (<= A -1.65e-7)
     t_0
     (if (<= A -1.12e-183)
       (* 180.0 (/ (atan (/ (- C B) B)) PI))
       (if (<= A -1.3e-234)
         t_0
         (if (<= A -1.1e-286)
           (/ (* 180.0 (atan (/ 1.0 (- -1.0 (/ C B))))) PI)
           (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -1.65e-7) {
		tmp = t_0;
	} else if (A <= -1.12e-183) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= -1.3e-234) {
		tmp = t_0;
	} else if (A <= -1.1e-286) {
		tmp = (180.0 * atan((1.0 / (-1.0 - (C / B))))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -1.65e-7) {
		tmp = t_0;
	} else if (A <= -1.12e-183) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= -1.3e-234) {
		tmp = t_0;
	} else if (A <= -1.1e-286) {
		tmp = (180.0 * Math.atan((1.0 / (-1.0 - (C / B))))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	tmp = 0
	if A <= -1.65e-7:
		tmp = t_0
	elif A <= -1.12e-183:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= -1.3e-234:
		tmp = t_0
	elif A <= -1.1e-286:
		tmp = (180.0 * math.atan((1.0 / (-1.0 - (C / B))))) / math.pi
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))))
	tmp = 0.0
	if (A <= -1.65e-7)
		tmp = t_0;
	elseif (A <= -1.12e-183)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= -1.3e-234)
		tmp = t_0;
	elseif (A <= -1.1e-286)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(-1.0 - Float64(C / B))))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	tmp = 0.0;
	if (A <= -1.65e-7)
		tmp = t_0;
	elseif (A <= -1.12e-183)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= -1.3e-234)
		tmp = t_0;
	elseif (A <= -1.1e-286)
		tmp = (180.0 * atan((1.0 / (-1.0 - (C / B))))) / pi;
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.65e-7], t$95$0, If[LessEqual[A, -1.12e-183], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.3e-234], t$95$0, If[LessEqual[A, -1.1e-286], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(-1.0 - N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.6500000000000001e-7 or -1.1199999999999999e-183 < A < -1.29999999999999995e-234

   1. Initial program 27.9%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in B around 0 77.0%

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

   if -1.6500000000000001e-7 < A < -1.1199999999999999e-183

   1. Initial program 70.4%

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

   3. Taylor expanded in A around 0 68.6%

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

      1. unpow2 68.6%

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

      2. unpow2 68.6%

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

      3. hypot-define 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in C around 0 65.7%

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

   if -1.29999999999999995e-234 < A < -1.1e-286

   1. Initial program 60.8%

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

      1. associate-*r/ 60.8%

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

      2. associate-*l/ 60.9%

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

      3. *-un-lft-identity 60.9%

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

      4. unpow2 60.9%

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

      5. unpow2 60.9%

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

      6. hypot-define 89.8%

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

   4. Applied egg-rr 89.8%

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

      1. clear-num 89.8%

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

      2. associate--l- 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in A around 0 60.9%

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

      1. unpow2 60.9%

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

      2. unpow2 60.9%

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

      3. hypot-undefine 89.8%

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

   9. Simplified 89.8%

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

   10. Taylor expanded in B around inf 79.5%

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

       1. sub-neg 79.5%

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

       2. metadata-eval 79.5%

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

       3. +-commutative 79.5%

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

       4. associate-*r/ 79.5%

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

       5. mul-1-neg 79.5%

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

   12. Simplified 79.5%

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

   if -1.1e-286 < A

   1. Initial program 71.5%

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

      1. associate-*r/ 71.6%

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

      2. associate-*l/ 71.6%

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

      3. *-un-lft-identity 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-define 90.9%

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

   4. Applied egg-rr 90.9%

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

   5. Taylor expanded in B around -inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. div-sub 69.6%

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

   7. Simplified 69.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.12 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-234}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-1 - \frac{C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{if}\;A \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -1.15 \cdot 10^{-183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))))
   (if (<= A -4.3e-10)
     t_1
     (if (<= A -1.15e-183)
       t_0
       (if (<= A -7.5e-226)
         t_1
         (if (<= A -5.2e-289)
           t_0
           (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -4.3e-10) {
		tmp = t_1;
	} else if (A <= -1.15e-183) {
		tmp = t_0;
	} else if (A <= -7.5e-226) {
		tmp = t_1;
	} else if (A <= -5.2e-289) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -4.3e-10) {
		tmp = t_1;
	} else if (A <= -1.15e-183) {
		tmp = t_0;
	} else if (A <= -7.5e-226) {
		tmp = t_1;
	} else if (A <= -5.2e-289) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	tmp = 0
	if A <= -4.3e-10:
		tmp = t_1
	elif A <= -1.15e-183:
		tmp = t_0
	elif A <= -7.5e-226:
		tmp = t_1
	elif A <= -5.2e-289:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))))
	tmp = 0.0
	if (A <= -4.3e-10)
		tmp = t_1;
	elseif (A <= -1.15e-183)
		tmp = t_0;
	elseif (A <= -7.5e-226)
		tmp = t_1;
	elseif (A <= -5.2e-289)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	tmp = 0.0;
	if (A <= -4.3e-10)
		tmp = t_1;
	elseif (A <= -1.15e-183)
		tmp = t_0;
	elseif (A <= -7.5e-226)
		tmp = t_1;
	elseif (A <= -5.2e-289)
		tmp = t_0;
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -4.3e-10], t$95$1, If[LessEqual[A, -1.15e-183], t$95$0, If[LessEqual[A, -7.5e-226], t$95$1, If[LessEqual[A, -5.2e-289], t$95$0, N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.30000000000000014e-10 or -1.15000000000000008e-183 < A < -7.50000000000000044e-226

   1. Initial program 26.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in B around 0 78.5%

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

   if -4.30000000000000014e-10 < A < -1.15000000000000008e-183 or -7.50000000000000044e-226 < A < -5.1999999999999998e-289

   1. Initial program 67.4%

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

   3. Taylor expanded in A around 0 66.0%

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

      1. unpow2 66.0%

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

      2. unpow2 66.0%

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

      3. hypot-define 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in C around 0 66.6%

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

   if -5.1999999999999998e-289 < A

   1. Initial program 71.5%

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

      1. associate-*r/ 71.6%

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

      2. associate-*l/ 71.6%

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

      3. *-un-lft-identity 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-define 90.9%

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

   4. Applied egg-rr 90.9%

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

   5. Taylor expanded in B around -inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. div-sub 69.6%

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

   7. Simplified 69.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.15 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-226}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{if}\;A \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -3.15 \cdot 10^{-183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -1.18 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-288}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C B) B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))))
   (if (<= A -2.15e-10)
     t_1
     (if (<= A -3.15e-183)
       t_0
       (if (<= A -1.18e-225)
         t_1
         (if (<= A -2.2e-288)
           t_0
           (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -2.15e-10) {
		tmp = t_1;
	} else if (A <= -3.15e-183) {
		tmp = t_0;
	} else if (A <= -1.18e-225) {
		tmp = t_1;
	} else if (A <= -2.2e-288) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	double tmp;
	if (A <= -2.15e-10) {
		tmp = t_1;
	} else if (A <= -3.15e-183) {
		tmp = t_0;
	} else if (A <= -1.18e-225) {
		tmp = t_1;
	} else if (A <= -2.2e-288) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	tmp = 0
	if A <= -2.15e-10:
		tmp = t_1
	elif A <= -3.15e-183:
		tmp = t_0
	elif A <= -1.18e-225:
		tmp = t_1
	elif A <= -2.2e-288:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))))
	tmp = 0.0
	if (A <= -2.15e-10)
		tmp = t_1;
	elseif (A <= -3.15e-183)
		tmp = t_0;
	elseif (A <= -1.18e-225)
		tmp = t_1;
	elseif (A <= -2.2e-288)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - B) / B)) / pi);
	t_1 = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	tmp = 0.0;
	if (A <= -2.15e-10)
		tmp = t_1;
	elseif (A <= -3.15e-183)
		tmp = t_0;
	elseif (A <= -1.18e-225)
		tmp = t_1;
	elseif (A <= -2.2e-288)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.15e-10], t$95$1, If[LessEqual[A, -3.15e-183], t$95$0, If[LessEqual[A, -1.18e-225], t$95$1, If[LessEqual[A, -2.2e-288], t$95$0, N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.15000000000000007e-10 or -3.1499999999999999e-183 < A < -1.18e-225

   1. Initial program 26.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in B around 0 78.5%

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

   if -2.15000000000000007e-10 < A < -3.1499999999999999e-183 or -1.18e-225 < A < -2.2000000000000002e-288

   1. Initial program 67.4%

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

   3. Taylor expanded in A around 0 66.0%

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

      1. unpow2 66.0%

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

      2. unpow2 66.0%

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

      3. hypot-define 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in C around 0 66.6%

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

   if -2.2000000000000002e-288 < A

   1. Initial program 71.5%

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

   3. Taylor expanded in B around -inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. div-sub 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -3.15 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.18 \cdot 10^{-225}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-288}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{+135}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))))
   (if (<= A -6.8e-63)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -1.3e-181)
       t_0
       (if (<= A -3.1e-273)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= A 4.4e+135) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double tmp;
	if (A <= -6.8e-63) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.3e-181) {
		tmp = t_0;
	} else if (A <= -3.1e-273) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (A <= 4.4e+135) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double tmp;
	if (A <= -6.8e-63) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.3e-181) {
		tmp = t_0;
	} else if (A <= -3.1e-273) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (A <= 4.4e+135) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	tmp = 0
	if A <= -6.8e-63:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.3e-181:
		tmp = t_0
	elif A <= -3.1e-273:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif A <= 4.4e+135:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	tmp = 0.0
	if (A <= -6.8e-63)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.3e-181)
		tmp = t_0;
	elseif (A <= -3.1e-273)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (A <= 4.4e+135)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + (C / B))) / pi);
	tmp = 0.0;
	if (A <= -6.8e-63)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.3e-181)
		tmp = t_0;
	elseif (A <= -3.1e-273)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (A <= 4.4e+135)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -6.8e-63], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.3e-181], t$95$0, If[LessEqual[A, -3.1e-273], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.4e+135], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -6.79999999999999997e-63

   1. Initial program 27.0%

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

   3. Taylor expanded in A around -inf 65.0%

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

   if -6.79999999999999997e-63 < A < -1.29999999999999999e-181 or -3.09999999999999988e-273 < A < 4.3999999999999999e135

   1. Initial program 70.1%

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

   3. Taylor expanded in B around -inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. div-sub 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in C around inf 57.4%

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

   if -1.29999999999999999e-181 < A < -3.09999999999999988e-273

   1. Initial program 44.1%

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

   3. Taylor expanded in C around inf 46.4%

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

   4. Taylor expanded in A around inf 54.6%

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

   if 4.3999999999999999e135 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in A around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

   5. Simplified 80.8%

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

Alternative 13: 53.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -8 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-272}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))))
   (if (<= A -8e-64)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -1.1e-183)
       t_0
       (if (<= A -1.3e-272)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= A 9e+132) t_0 (* 180.0 (/ (atan (/ A (- B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double tmp;
	if (A <= -8e-64) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.1e-183) {
		tmp = t_0;
	} else if (A <= -1.3e-272) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (A <= 9e+132) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double tmp;
	if (A <= -8e-64) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.1e-183) {
		tmp = t_0;
	} else if (A <= -1.3e-272) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (A <= 9e+132) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	tmp = 0
	if A <= -8e-64:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.1e-183:
		tmp = t_0
	elif A <= -1.3e-272:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif A <= 9e+132:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	tmp = 0.0
	if (A <= -8e-64)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.1e-183)
		tmp = t_0;
	elseif (A <= -1.3e-272)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (A <= 9e+132)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + (C / B))) / pi);
	tmp = 0.0;
	if (A <= -8e-64)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.1e-183)
		tmp = t_0;
	elseif (A <= -1.3e-272)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (A <= 9e+132)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((A / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -8e-64], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.1e-183], t$95$0, If[LessEqual[A, -1.3e-272], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], t$95$0, N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7.99999999999999972e-64

   1. Initial program 27.0%

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

   3. Taylor expanded in A around -inf 65.0%

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

   if -7.99999999999999972e-64 < A < -1.1e-183 or -1.29999999999999996e-272 < A < 8.99999999999999944e132

   1. Initial program 70.1%

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

   3. Taylor expanded in B around -inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. div-sub 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in C around inf 57.4%

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

   if -1.1e-183 < A < -1.29999999999999996e-272

   1. Initial program 44.1%

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

   3. Taylor expanded in C around inf 46.4%

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

   4. Taylor expanded in A around inf 54.6%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in B around inf 85.4%

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

   4. Taylor expanded in A around inf 80.8%

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

      1. mul-1-neg 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.1 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-272}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{A}{B}\\ \mathbf{if}\;C \leq -6.3 \cdot 10^{-165}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot t\_0}{B}\right)\\ \mathbf{elif}\;C \leq -2.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{t\_0}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t\_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ A B))))
   (if (<= C -6.3e-165)
     (* (/ 180.0 PI) (atan (/ (+ C (* B t_0)) B)))
     (if (<= C -2.5e-240)
       (/ (* 180.0 (atan (/ -1.0 t_0))) PI)
       (if (<= C 2.75e-61)
         (* 180.0 (/ (atan t_0) PI))
         (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -6.3e-165) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B * t_0)) / B));
	} else if (C <= -2.5e-240) {
		tmp = (180.0 * atan((-1.0 / t_0))) / ((double) M_PI);
	} else if (C <= 2.75e-61) {
		tmp = 180.0 * (atan(t_0) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -6.3e-165) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B * t_0)) / B));
	} else if (C <= -2.5e-240) {
		tmp = (180.0 * Math.atan((-1.0 / t_0))) / Math.PI;
	} else if (C <= 2.75e-61) {
		tmp = 180.0 * (Math.atan(t_0) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = -1.0 - (A / B)
	tmp = 0
	if C <= -6.3e-165:
		tmp = (180.0 / math.pi) * math.atan(((C + (B * t_0)) / B))
	elif C <= -2.5e-240:
		tmp = (180.0 * math.atan((-1.0 / t_0))) / math.pi
	elif C <= 2.75e-61:
		tmp = 180.0 * (math.atan(t_0) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(-1.0 - Float64(A / B))
	tmp = 0.0
	if (C <= -6.3e-165)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B * t_0)) / B)));
	elseif (C <= -2.5e-240)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 / t_0))) / pi);
	elseif (C <= 2.75e-61)
		tmp = Float64(180.0 * Float64(atan(t_0) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = -1.0 - (A / B);
	tmp = 0.0;
	if (C <= -6.3e-165)
		tmp = (180.0 / pi) * atan(((C + (B * t_0)) / B));
	elseif (C <= -2.5e-240)
		tmp = (180.0 * atan((-1.0 / t_0))) / pi;
	elseif (C <= 2.75e-61)
		tmp = 180.0 * (atan(t_0) / pi);
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -6.3e-165], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B * t$95$0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.5e-240], N[(N[(180.0 * N[ArcTan[N[(-1.0 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.75e-61], N[(180.0 * N[(N[ArcTan[t$95$0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -6.3000000000000001e-165

   1. Initial program 72.9%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in B around inf 74.2%

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

   if -6.3000000000000001e-165 < C < -2.5000000000000002e-240

   1. Initial program 63.1%

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

      1. associate-*r/ 63.1%

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

      2. associate-*l/ 63.1%

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

      3. *-un-lft-identity 63.1%

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

      4. unpow2 63.1%

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

      5. unpow2 63.1%

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

      6. hypot-define 83.1%

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

   4. Applied egg-rr 83.1%

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

      1. clear-num 83.1%

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

      2. associate--l- 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in B around -inf 62.6%

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

      1. associate-*r/ 62.6%

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

      2. mul-1-neg 62.6%

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

   9. Simplified 62.6%

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

   10. Taylor expanded in C around 0 62.6%

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

   if -2.5000000000000002e-240 < C < 2.7499999999999998e-61

   1. Initial program 66.5%

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

   3. Taylor expanded in B around inf 61.2%

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

   4. Taylor expanded in C around 0 61.2%

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

      1. neg-mul-1 61.2%

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

      2. distribute-neg-in 61.2%

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

      3. metadata-eval 61.2%

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

   6. Simplified 61.2%

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

   if 2.7499999999999998e-61 < C

   1. Initial program 27.7%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in B around 0 73.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -6.3 \cdot 10^{-165}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \mathbf{elif}\;C \leq -2.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{-1 - \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{A}{B}\\ \mathbf{if}\;C \leq -6.3 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B} + t\_0\right)}}\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{t\_0}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.85 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t\_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ A B))))
   (if (<= C -6.3e-165)
     (* 180.0 (/ 1.0 (/ PI (atan (+ (/ C B) t_0)))))
     (if (<= C -8e-240)
       (/ (* 180.0 (atan (/ -1.0 t_0))) PI)
       (if (<= C 2.85e-61)
         (* 180.0 (/ (atan t_0) PI))
         (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -6.3e-165) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan(((C / B) + t_0))));
	} else if (C <= -8e-240) {
		tmp = (180.0 * atan((-1.0 / t_0))) / ((double) M_PI);
	} else if (C <= 2.85e-61) {
		tmp = 180.0 * (atan(t_0) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -6.3e-165) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan(((C / B) + t_0))));
	} else if (C <= -8e-240) {
		tmp = (180.0 * Math.atan((-1.0 / t_0))) / Math.PI;
	} else if (C <= 2.85e-61) {
		tmp = 180.0 * (Math.atan(t_0) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = -1.0 - (A / B)
	tmp = 0
	if C <= -6.3e-165:
		tmp = 180.0 * (1.0 / (math.pi / math.atan(((C / B) + t_0))))
	elif C <= -8e-240:
		tmp = (180.0 * math.atan((-1.0 / t_0))) / math.pi
	elif C <= 2.85e-61:
		tmp = 180.0 * (math.atan(t_0) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(-1.0 - Float64(A / B))
	tmp = 0.0
	if (C <= -6.3e-165)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(Float64(C / B) + t_0)))));
	elseif (C <= -8e-240)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 / t_0))) / pi);
	elseif (C <= 2.85e-61)
		tmp = Float64(180.0 * Float64(atan(t_0) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = -1.0 - (A / B);
	tmp = 0.0;
	if (C <= -6.3e-165)
		tmp = 180.0 * (1.0 / (pi / atan(((C / B) + t_0))));
	elseif (C <= -8e-240)
		tmp = (180.0 * atan((-1.0 / t_0))) / pi;
	elseif (C <= 2.85e-61)
		tmp = 180.0 * (atan(t_0) / pi);
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -6.3e-165], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(N[(C / B), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -8e-240], N[(N[(180.0 * N[ArcTan[N[(-1.0 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.85e-61], N[(180.0 * N[(N[ArcTan[t$95$0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -6.3000000000000001e-165

   1. Initial program 72.9%

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

   3. Taylor expanded in B around inf 74.1%

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

      1. clear-num 74.1%

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

   5. Applied egg-rr 74.1%

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

   if -6.3000000000000001e-165 < C < -7.9999999999999998e-240

   1. Initial program 63.1%

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

      1. associate-*r/ 63.1%

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

      2. associate-*l/ 63.1%

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

      3. *-un-lft-identity 63.1%

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

      4. unpow2 63.1%

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

      5. unpow2 63.1%

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

      6. hypot-define 83.1%

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

   4. Applied egg-rr 83.1%

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

      1. clear-num 83.1%

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

      2. associate--l- 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in B around -inf 62.6%

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

      1. associate-*r/ 62.6%

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

      2. mul-1-neg 62.6%

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

   9. Simplified 62.6%

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

   10. Taylor expanded in C around 0 62.6%

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

   if -7.9999999999999998e-240 < C < 2.85000000000000003e-61

   1. Initial program 66.5%

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

   3. Taylor expanded in B around inf 61.2%

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

   4. Taylor expanded in C around 0 61.2%

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

      1. neg-mul-1 61.2%

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

      2. distribute-neg-in 61.2%

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

      3. metadata-eval 61.2%

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

   6. Simplified 61.2%

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

   if 2.85000000000000003e-61 < C

   1. Initial program 27.7%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in B around 0 73.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -6.3 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}}\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-240}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{-1 - \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.85 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{A}{B}\\ \mathbf{if}\;C \leq -1.5 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + t\_0\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-239}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{t\_0}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} t\_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ A B))))
   (if (<= C -1.5e-165)
     (* 180.0 (/ (atan (+ (/ C B) t_0)) PI))
     (if (<= C -1e-239)
       (/ (* 180.0 (atan (/ -1.0 t_0))) PI)
       (if (<= C 2.5e-61)
         (* 180.0 (/ (atan t_0) PI))
         (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -1.5e-165) {
		tmp = 180.0 * (atan(((C / B) + t_0)) / ((double) M_PI));
	} else if (C <= -1e-239) {
		tmp = (180.0 * atan((-1.0 / t_0))) / ((double) M_PI);
	} else if (C <= 2.5e-61) {
		tmp = 180.0 * (atan(t_0) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = -1.0 - (A / B);
	double tmp;
	if (C <= -1.5e-165) {
		tmp = 180.0 * (Math.atan(((C / B) + t_0)) / Math.PI);
	} else if (C <= -1e-239) {
		tmp = (180.0 * Math.atan((-1.0 / t_0))) / Math.PI;
	} else if (C <= 2.5e-61) {
		tmp = 180.0 * (Math.atan(t_0) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = -1.0 - (A / B)
	tmp = 0
	if C <= -1.5e-165:
		tmp = 180.0 * (math.atan(((C / B) + t_0)) / math.pi)
	elif C <= -1e-239:
		tmp = (180.0 * math.atan((-1.0 / t_0))) / math.pi
	elif C <= 2.5e-61:
		tmp = 180.0 * (math.atan(t_0) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(-1.0 - Float64(A / B))
	tmp = 0.0
	if (C <= -1.5e-165)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + t_0)) / pi));
	elseif (C <= -1e-239)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 / t_0))) / pi);
	elseif (C <= 2.5e-61)
		tmp = Float64(180.0 * Float64(atan(t_0) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = -1.0 - (A / B);
	tmp = 0.0;
	if (C <= -1.5e-165)
		tmp = 180.0 * (atan(((C / B) + t_0)) / pi);
	elseif (C <= -1e-239)
		tmp = (180.0 * atan((-1.0 / t_0))) / pi;
	elseif (C <= 2.5e-61)
		tmp = 180.0 * (atan(t_0) / pi);
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.5e-165], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1e-239], N[(N[(180.0 * N[ArcTan[N[(-1.0 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.5e-61], N[(180.0 * N[(N[ArcTan[t$95$0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.49999999999999989e-165

   1. Initial program 72.9%

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

   3. Taylor expanded in B around inf 74.1%

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

   if -1.49999999999999989e-165 < C < -1.0000000000000001e-239

   1. Initial program 63.1%

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

      1. associate-*r/ 63.1%

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

      2. associate-*l/ 63.1%

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

      3. *-un-lft-identity 63.1%

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

      4. unpow2 63.1%

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

      5. unpow2 63.1%

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

      6. hypot-define 83.1%

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

   4. Applied egg-rr 83.1%

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

      1. clear-num 83.1%

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

      2. associate--l- 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in B around -inf 62.6%

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

      1. associate-*r/ 62.6%

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

      2. mul-1-neg 62.6%

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

   9. Simplified 62.6%

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

   10. Taylor expanded in C around 0 62.6%

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

   if -1.0000000000000001e-239 < C < 2.4999999999999999e-61

   1. Initial program 66.5%

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

   3. Taylor expanded in B around inf 61.2%

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

   4. Taylor expanded in C around 0 61.2%

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

      1. neg-mul-1 61.2%

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

      2. distribute-neg-in 61.2%

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

      3. metadata-eval 61.2%

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

   6. Simplified 61.2%

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

   if 2.4999999999999999e-61 < C

   1. Initial program 27.7%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in B around 0 73.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-239}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{-1 - \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.2e-7)
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)
   (if (<= A -3.7e-289)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 9e+132)
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.2e-7) {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	} else if (A <= -3.7e-289) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 9e+132) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.2e-7) {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	} else if (A <= -3.7e-289) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 9e+132) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.2e-7:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	elif A <= -3.7e-289:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 9e+132:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.2e-7)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	elseif (A <= -3.7e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 9e+132)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.2e-7)
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	elseif (A <= -3.7e-289)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 9e+132)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.2e-7], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -3.7e-289], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.2000000000000001e-7

   1. Initial program 23.6%

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

      1. associate-*r/ 23.6%

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

      2. associate-*l/ 23.6%

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

      3. *-un-lft-identity 23.6%

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

      4. unpow2 23.6%

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

      5. unpow2 23.6%

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

      6. hypot-define 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in A around -inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*r/ 69.7%

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

   7. Applied egg-rr 69.7%

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

   if -2.2000000000000001e-7 < A < -3.69999999999999989e-289

   1. Initial program 62.3%

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

   3. Taylor expanded in A around 0 61.2%

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

      1. unpow2 61.2%

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

      2. unpow2 61.2%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in C around 0 60.0%

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

   if -3.69999999999999989e-289 < A < 8.99999999999999944e132

   1. Initial program 67.7%

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

      1. associate-*r/ 67.7%

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

      2. associate-*l/ 67.7%

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

      3. *-un-lft-identity 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-define 88.6%

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

   4. Applied egg-rr 88.6%

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

      1. clear-num 88.6%

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

      2. associate--l- 88.6%

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

   6. Applied egg-rr 88.6%

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

   7. Taylor expanded in A around 0 59.6%

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

      1. unpow2 59.6%

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

      2. unpow2 59.6%

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

      3. hypot-undefine 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in B around -inf 56.7%

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

       1. +-commutative 56.7%

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

   12. Simplified 56.7%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in A around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{-8}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-286}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e-8)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A -5e-286)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 9e+132)
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e-8) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -5e-286) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 9e+132) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e-8) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -5e-286) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 9e+132) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e-8:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -5e-286:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 9e+132:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e-8)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -5e-286)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 9e+132)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e-8)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -5e-286)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 9e+132)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e-8], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -5e-286], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.55e-8

   1. Initial program 23.6%

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

      1. associate-*r/ 23.6%

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

      2. associate-*l/ 23.6%

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

      3. *-un-lft-identity 23.6%

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

      4. unpow2 23.6%

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

      5. unpow2 23.6%

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

      6. hypot-define 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in A around -inf 69.7%

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

   if -1.55e-8 < A < -5.00000000000000037e-286

   1. Initial program 62.3%

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

   3. Taylor expanded in A around 0 61.2%

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

      1. unpow2 61.2%

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

      2. unpow2 61.2%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in C around 0 60.0%

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

   if -5.00000000000000037e-286 < A < 8.99999999999999944e132

   1. Initial program 67.7%

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

      1. associate-*r/ 67.7%

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

      2. associate-*l/ 67.7%

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

      3. *-un-lft-identity 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-define 88.6%

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

   4. Applied egg-rr 88.6%

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

      1. clear-num 88.6%

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

      2. associate--l- 88.6%

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

   6. Applied egg-rr 88.6%

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

   7. Taylor expanded in A around 0 59.6%

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

      1. unpow2 59.6%

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

      2. unpow2 59.6%

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

      3. hypot-undefine 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in B around -inf 56.7%

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

       1. +-commutative 56.7%

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

   12. Simplified 56.7%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in A around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{-8}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-286}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{-8}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{-288}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e-8)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A -3.8e-288)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 9e+132)
       (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e-8) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -3.8e-288) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 9e+132) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e-8) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -3.8e-288) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 9e+132) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8e-8:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -3.8e-288:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 9e+132:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8e-8)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -3.8e-288)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 9e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8e-8)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -3.8e-288)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 9e+132)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8e-8], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -3.8e-288], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -8.0000000000000002e-8

   1. Initial program 23.6%

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

      1. associate-*r/ 23.6%

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

      2. associate-*l/ 23.6%

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

      3. *-un-lft-identity 23.6%

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

      4. unpow2 23.6%

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

      5. unpow2 23.6%

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

      6. hypot-define 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in A around -inf 69.7%

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

   if -8.0000000000000002e-8 < A < -3.7999999999999998e-288

   1. Initial program 62.3%

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

   3. Taylor expanded in A around 0 61.2%

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

      1. unpow2 61.2%

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

      2. unpow2 61.2%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in C around 0 60.0%

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

   if -3.7999999999999998e-288 < A < 8.99999999999999944e132

   1. Initial program 67.7%

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

   3. Taylor expanded in B around -inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. div-sub 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in C around inf 56.7%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in A around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

   5. Simplified 80.8%

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

Alternative 20: 55.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-287}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.4e-8)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A -6e-287)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 9e+132)
       (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e-8) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -6e-287) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 9e+132) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e-8) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -6e-287) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 9e+132) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.4e-8:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -6e-287:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 9e+132:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.4e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -6e-287)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 9e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.4e-8)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -6e-287)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 9e+132)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.4e-8], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -6e-287], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+132], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.3999999999999997e-8

   1. Initial program 23.6%

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

   3. Taylor expanded in A around -inf 69.6%

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

   if -4.3999999999999997e-8 < A < -5.99999999999999984e-287

   1. Initial program 62.3%

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

   3. Taylor expanded in A around 0 61.2%

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

      1. unpow2 61.2%

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

      2. unpow2 61.2%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in C around 0 60.0%

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

   if -5.99999999999999984e-287 < A < 8.99999999999999944e132

   1. Initial program 67.7%

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

   3. Taylor expanded in B around -inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. div-sub 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in C around inf 56.7%

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

   if 8.99999999999999944e132 < A

   1. Initial program 82.0%

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

   3. Taylor expanded in A around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. *-commutative 80.8%

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

   5. Simplified 80.8%

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

Alternative 21: 48.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.8 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5.8e-69)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C -6.8e-240)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= C 4.2e-74)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.8e-69) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -6.8e-240) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (C <= 4.2e-74) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.8e-69) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -6.8e-240) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (C <= 4.2e-74) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5.8e-69:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -6.8e-240:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif C <= 4.2e-74:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5.8e-69)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -6.8e-240)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (C <= 4.2e-74)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5.8e-69)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -6.8e-240)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (C <= 4.2e-74)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5.8e-69], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -6.8e-240], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.2e-74], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -5.7999999999999997e-69

   1. Initial program 77.5%

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

   3. Taylor expanded in C around -inf 66.2%

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

   if -5.7999999999999997e-69 < C < -6.79999999999999979e-240

   1. Initial program 59.2%

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

   3. Taylor expanded in A around -inf 44.4%

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

   if -6.79999999999999979e-240 < C < 4.2e-74

   1. Initial program 66.2%

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

   3. Taylor expanded in B around inf 38.6%

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

   if 4.2e-74 < C

   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. Add Preprocessing

   3. Taylor expanded in C around inf 52.3%

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

   4. Taylor expanded in A around inf 63.3%

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

Alternative 22: 48.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.3 \cdot 10^{-69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.26 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.4 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.3e-69)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -1.26e-241)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= C 5.4e-73)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.3e-69) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -1.26e-241) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (C <= 5.4e-73) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.3e-69) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -1.26e-241) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (C <= 5.4e-73) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.3e-69:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -1.26e-241:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif C <= 5.4e-73:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.3e-69)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -1.26e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (C <= 5.4e-73)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.3e-69)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -1.26e-241)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (C <= 5.4e-73)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.3e-69], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.26e-241], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.4e-73], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -3.3e-69

   1. Initial program 77.5%

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

   3. Taylor expanded in B around inf 82.0%

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

   4. Taylor expanded in C around inf 65.8%

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

   if -3.3e-69 < C < -1.26e-241

   1. Initial program 59.2%

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

   3. Taylor expanded in A around -inf 44.4%

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

   if -1.26e-241 < C < 5.39999999999999989e-73

   1. Initial program 66.2%

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

   3. Taylor expanded in B around inf 38.6%

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

   if 5.39999999999999989e-73 < C

   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. Add Preprocessing

   3. Taylor expanded in C around inf 52.3%

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

   4. Taylor expanded in A around inf 63.3%

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

Alternative 23: 60.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-9}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5e-9)
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)
   (if (<= A -3.8e-289)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e-9) {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	} else if (A <= -3.8e-289) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e-9) {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	} else if (A <= -3.8e-289) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5e-9:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	elif A <= -3.8e-289:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5e-9)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	elseif (A <= -3.8e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5e-9)
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	elseif (A <= -3.8e-289)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5e-9], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -3.8e-289], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.0000000000000001e-9

   1. Initial program 23.6%

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

      1. associate-*r/ 23.6%

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

      2. associate-*l/ 23.6%

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

      3. *-un-lft-identity 23.6%

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

      4. unpow2 23.6%

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

      5. unpow2 23.6%

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

      6. hypot-define 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in A around -inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*r/ 69.7%

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

   7. Applied egg-rr 69.7%

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

   if -5.0000000000000001e-9 < A < -3.80000000000000009e-289

   1. Initial program 62.3%

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

   3. Taylor expanded in A around 0 61.2%

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

      1. unpow2 61.2%

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

      2. unpow2 61.2%

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

      3. hypot-define 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in C around 0 60.0%

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

   if -3.80000000000000009e-289 < A

   1. Initial program 71.5%

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

   3. Taylor expanded in B around -inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. div-sub 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-9}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.8 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 59.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.7 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.7e+16)
   (* 180.0 (/ (atan (/ (- C B) B)) PI))
   (if (<= C 2.8e-61)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (/ (* 180.0 (atan (* B (/ -0.5 C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.7e+16) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 2.8e-61) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((B * (-0.5 / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.7e+16) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 2.8e-61) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((B * (-0.5 / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.7e+16:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 2.8e-61:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan((B * (-0.5 / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.7e+16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 2.8e-61)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(-0.5 / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.7e+16)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 2.8e-61)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = (180.0 * atan((B * (-0.5 / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.7e+16], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.8e-61], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.7e16

   1. Initial program 79.4%

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

   3. Taylor expanded in A around 0 79.4%

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

      1. unpow2 79.4%

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

      2. unpow2 79.4%

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

      3. hypot-define 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in C around 0 85.4%

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

   if -4.7e16 < C < 2.8000000000000001e-61

   1. Initial program 64.5%

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

   3. Taylor expanded in B around inf 55.0%

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

   4. Taylor expanded in C around 0 54.0%

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

      1. neg-mul-1 54.0%

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

      2. distribute-neg-in 54.0%

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

      3. metadata-eval 54.0%

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

   6. Simplified 54.0%

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

   if 2.8000000000000001e-61 < C

   1. Initial program 27.7%

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

      1. associate-*r/ 27.7%

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

      2. associate-*l/ 27.7%

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

      3. *-un-lft-identity 27.7%

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

      4. unpow2 27.7%

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

      5. unpow2 27.7%

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

      6. hypot-define 51.4%

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

   4. Applied egg-rr 51.4%

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

      1. clear-num 51.4%

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

      2. associate--l- 48.3%

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

   6. Applied egg-rr 48.3%

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

   7. Taylor expanded in A around 0 21.8%

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

      1. unpow2 21.8%

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

      2. unpow2 21.8%

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

      3. hypot-undefine 41.4%

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

   9. Simplified 41.4%

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

   10. Taylor expanded in B around 0 64.3%

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

       1. associate-*r/ 64.3%

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

       2. *-commutative 64.3%

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

       3. associate-/l* 64.2%

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

   12. Simplified 64.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.7 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 47.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.8 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.8e+16)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C 1.25e-73)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+16) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 1.25e-73) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+16) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 1.25e-73) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.8e+16:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 1.25e-73:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.8e+16)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 1.25e-73)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.8e+16)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 1.25e-73)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.8e+16], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.25e-73], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.8e16

   1. Initial program 79.4%

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

   3. Taylor expanded in B around inf 85.1%

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

   4. Taylor expanded in C around inf 74.4%

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

   if -4.8e16 < C < 1.25e-73

   1. Initial program 64.3%

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

   3. Taylor expanded in B around inf 34.4%

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

   if 1.25e-73 < C

   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. Add Preprocessing

   3. Taylor expanded in C around inf 52.3%

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

   4. Taylor expanded in A around inf 63.3%

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

Alternative 26: 47.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-93)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.2e-28)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-93) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.2e-28) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-93) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.2e-28) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-93:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.2e-28:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-93)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.2e-28)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-93)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.2e-28)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-93], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.2e-28], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.5999999999999998e-93

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 50.6%

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

   if -2.5999999999999998e-93 < B < 8.2000000000000005e-28

   1. Initial program 60.6%

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

   3. Taylor expanded in B around inf 52.7%

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

   4. Taylor expanded in C around inf 39.7%

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

   if 8.2000000000000005e-28 < B

   1. Initial program 55.9%

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

   3. Taylor expanded in B around inf 62.5%

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

Alternative 27: 45.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-177}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.2e-177)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.4e-127)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-177) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.4e-127) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-177) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.4e-127) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.2e-177:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.4e-127:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.2e-177)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.4e-127)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.2e-177)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.4e-127)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.2e-177], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.4e-127], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1999999999999999e-177

   1. Initial program 59.4%

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

   3. Taylor expanded in B around -inf 47.1%

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

   if -1.1999999999999999e-177 < B < 5.3999999999999999e-127

   1. Initial program 54.6%

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

   3. Taylor expanded in C around inf 38.6%

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

      1. associate-*r/ 38.6%

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

      2. mul-1-neg 38.6%

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

      3. distribute-rgt1-in 38.6%

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

      4. metadata-eval 38.6%

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

      5. mul0-lft 38.6%

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

      6. metadata-eval 38.6%

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

   5. Simplified 38.6%

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

   if 5.3999999999999999e-127 < B

   1. Initial program 57.4%

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

   3. Taylor expanded in B around inf 52.3%

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

Alternative 28: 40.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 37.5%

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

   if -1.999999999999994e-310 < B

   1. Initial program 58.2%

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

   3. Taylor expanded in B around inf 41.8%

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

Alternative 29: 21.4% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 57.3%

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

3. Taylor expanded in B around inf 23.2%

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

Reproduce

herbie shell --seed 2024095 
(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)))