ABCF->ab-angle angle

Percentage Accurate: 53.5% → 81.5%

Time: 21.0s

Alternatives: 22

Speedup: 3.6×

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: 53.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e+90)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+90) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+90) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+90:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+90)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+90)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e+90], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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]]

Derivation

1. Split input into 2 regimes

2. if A < -1.15e90

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -1.15e90 < A

   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. Step-by-step derivation

      1. associate-*r/ 59.4%

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

      2. associate-*l/ 59.4%

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

      3. *-un-lft-identity 59.4%

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

      4. unpow2 59.4%

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

      5. unpow2 59.4%

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

      6. hypot-define 84.1%

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

   4. Applied egg-rr 84.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{\frac{B}{A + \mathsf{hypot}\left(B, A\right)}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4e+88)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (if (<= A 4.6e-48)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (/ (* 180.0 (atan (/ -1.0 (/ B (+ A (hypot B A)))))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+88) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else if (A <= 4.6e-48) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 / (B / (A + hypot(B, A)))))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+88) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else if (A <= 4.6e-48) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 / (B / (A + Math.hypot(B, A)))))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4e+88:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	elif A <= 4.6e-48:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 / (B / (A + math.hypot(B, A)))))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4e+88)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	elseif (A <= 4.6e-48)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 / Float64(B / Float64(A + hypot(B, A)))))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4e+88)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	elseif (A <= 4.6e-48)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = (180.0 * atan((-1.0 / (B / (A + hypot(B, A)))))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4e+88], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 4.6e-48], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 / N[(B / N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.99999999999999984e88

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -3.99999999999999984e88 < A < 4.6000000000000001e-48

   1. Initial program 53.1%

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

      1. associate-*r/ 53.1%

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

      2. associate-*l/ 53.1%

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

      3. *-un-lft-identity 53.1%

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

      4. unpow2 53.1%

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

      5. unpow2 53.1%

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

      6. hypot-define 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in A around 0 51.5%

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

      1. unpow2 51.5%

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

      2. unpow2 51.5%

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

      3. hypot-undefine 76.1%

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

   7. Simplified 76.1%

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

   if 4.6000000000000001e-48 < A

   1. Initial program 70.2%

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

      1. associate-*r/ 70.2%

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

      2. associate-*l/ 70.2%

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

      3. *-un-lft-identity 70.2%

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

      4. unpow2 70.2%

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

      5. unpow2 70.2%

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

      6. hypot-define 95.2%

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

   4. Applied egg-rr 95.2%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

      3. associate--l- 95.2%

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

   6. Applied egg-rr 95.2%

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

      1. unpow-1 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in C around 0 69.2%

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

       1. associate-*r/ 69.2%

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

       2. neg-mul-1 69.2%

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

       3. +-commutative 69.2%

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

       4. unpow2 69.2%

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

       5. unpow2 69.2%

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

       6. hypot-define 88.4%

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

   11. Simplified 88.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{\frac{B}{A + \mathsf{hypot}\left(B, A\right)}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-47}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2e+90)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (if (<= A 4.1e-47)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2e+90) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else if (A <= 4.1e-47) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2e+90) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else if (A <= 4.1e-47) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2e+90:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	elif A <= 4.1e-47:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2e+90)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	elseif (A <= 4.1e-47)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2e+90)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	elseif (A <= 4.1e-47)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2e+90], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 4.1e-47], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.99999999999999993e90

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -1.99999999999999993e90 < A < 4.10000000000000002e-47

   1. Initial program 53.1%

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

      1. associate-*r/ 53.1%

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

      2. associate-*l/ 53.1%

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

      3. *-un-lft-identity 53.1%

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

      4. unpow2 53.1%

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

      5. unpow2 53.1%

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

      6. hypot-define 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in A around 0 51.5%

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

      1. unpow2 51.5%

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

      2. unpow2 51.5%

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

      3. hypot-undefine 76.1%

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

   7. Simplified 76.1%

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

   if 4.10000000000000002e-47 < A

   1. Initial program 70.2%

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

   3. Taylor expanded in C around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. +-commutative 69.2%

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

      4. unpow2 69.2%

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

      5. unpow2 69.2%

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

      6. hypot-define 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-47}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.8e+90)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (if (<= A 9e+82)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e+90) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else if (A <= 9e+82) {
		tmp = (180.0 * atan(((C - hypot(B, 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 tmp;
	if (A <= -2.8e+90) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else if (A <= 9e+82) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, 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):
	tmp = 0
	if A <= -2.8e+90:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	elif A <= 9e+82:
		tmp = (180.0 * math.atan(((C - math.hypot(B, 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)
	tmp = 0.0
	if (A <= -2.8e+90)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	elseif (A <= 9e+82)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / 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 <= -2.8e+90)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	elseif (A <= 9e+82)
		tmp = (180.0 * atan(((C - hypot(B, C)) / 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, -2.8e+90], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 9e+82], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -2.8e90

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -2.8e90 < A < 8.9999999999999993e82

   1. Initial program 53.1%

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

      1. associate-*r/ 53.1%

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

      2. associate-*l/ 53.1%

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

      3. *-un-lft-identity 53.1%

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

      4. unpow2 53.1%

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

      5. unpow2 53.1%

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

      6. hypot-define 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in A around 0 48.0%

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

      1. unpow2 48.0%

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

      2. unpow2 48.0%

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

      3. hypot-undefine 75.6%

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

   7. Simplified 75.6%

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

   if 8.9999999999999993e82 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in B around -inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. div-sub 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+82}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.4e+90)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (if (<= A 1e+80)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e+90) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else if (A <= 1e+80) {
		tmp = 180.0 * (atan(((C - hypot(B, 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 tmp;
	if (A <= -2.4e+90) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else if (A <= 1e+80) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, 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):
	tmp = 0
	if A <= -2.4e+90:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	elif A <= 1e+80:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, 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)
	tmp = 0.0
	if (A <= -2.4e+90)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	elseif (A <= 1e+80)
		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(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.4e+90)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	elseif (A <= 1e+80)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / 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, -2.4e+90], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1e+80], 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[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.4000000000000001e90

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -2.4000000000000001e90 < A < 1e80

   1. Initial program 53.1%

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

   3. Taylor expanded in A around 0 48.0%

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

      1. unpow2 48.0%

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

      2. unpow2 48.0%

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

      3. hypot-define 75.6%

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

   5. Simplified 75.6%

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

   if 1e80 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in B around -inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. div-sub 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.8e+85)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+85) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+85) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e+85:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e+85)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e+85)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.8e+85], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.79999999999999992e85

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -3.79999999999999992e85 < A

   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. Step-by-step derivation

      1. associate-*l/ 59.4%

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

      2. *-lft-identity 59.4%

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

      3. +-commutative 59.4%

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

      4. unpow2 59.4%

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

      5. unpow2 59.4%

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

      6. hypot-define 84.1%

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

   3. Simplified 84.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e+85)
   (/
    (* 180.0 (atan (/ 1.0 (* A (- (* 2.0 (/ 1.0 B)) (* 2.0 (/ C (* A B))))))))
    PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+85) {
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+85) {
		tmp = (180.0 * Math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e+85:
		tmp = (180.0 * math.atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e+85)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(A * Float64(Float64(2.0 * Float64(1.0 / B)) - Float64(2.0 * Float64(C / Float64(A * B)))))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e+85)
		tmp = (180.0 * atan((1.0 / (A * ((2.0 * (1.0 / B)) - (2.0 * (C / (A * B)))))))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e+85], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(A * N[(N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(C / N[(A * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.34999999999999992e85

   1. Initial program 19.9%

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

      1. associate-*r/ 19.9%

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

      2. associate-*l/ 19.9%

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

      3. *-un-lft-identity 19.9%

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

      4. unpow2 19.9%

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

      5. unpow2 19.9%

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

      6. hypot-define 42.9%

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

   4. Applied egg-rr 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. associate--l- 22.5%

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

   6. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

   8. Simplified 22.5%

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

   9. Taylor expanded in A around -inf 86.8%

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

   if -1.34999999999999992e85 < A

   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. Step-by-step derivation

   3. Simplified 83.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+85}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{A \cdot \left(2 \cdot \frac{1}{B} - 2 \cdot \frac{C}{A \cdot B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.12 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-294}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B C)))))
   (if (<= A -2.8e-95)
     (/ (* 180.0 (atan (* B (/ 0.5 A)))) PI)
     (if (<= A -1.12e-126)
       (* 180.0 (/ t_0 PI))
       (if (<= A -5.5e-193)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= A 2.05e-294)
           (/ (* 180.0 t_0) PI)
           (if (<= A 1.45e+78)
             (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / C)));
	double tmp;
	if (A <= -2.8e-95) {
		tmp = (180.0 * atan((B * (0.5 / A)))) / ((double) M_PI);
	} else if (A <= -1.12e-126) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -5.5e-193) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 2.05e-294) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else if (A <= 1.45e+78) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / C)));
	double tmp;
	if (A <= -2.8e-95) {
		tmp = (180.0 * Math.atan((B * (0.5 / A)))) / Math.PI;
	} else if (A <= -1.12e-126) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -5.5e-193) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 2.05e-294) {
		tmp = (180.0 * t_0) / Math.PI;
	} else if (A <= 1.45e+78) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / C)))
	tmp = 0
	if A <= -2.8e-95:
		tmp = (180.0 * math.atan((B * (0.5 / A)))) / math.pi
	elif A <= -1.12e-126:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -5.5e-193:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 2.05e-294:
		tmp = (180.0 * t_0) / math.pi
	elif A <= 1.45e+78:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / C)))
	tmp = 0.0
	if (A <= -2.8e-95)
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(0.5 / A)))) / pi);
	elseif (A <= -1.12e-126)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -5.5e-193)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 2.05e-294)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	elseif (A <= 1.45e+78)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (A <= -2.8e-95)
		tmp = (180.0 * atan((B * (0.5 / A)))) / pi;
	elseif (A <= -1.12e-126)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -5.5e-193)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 2.05e-294)
		tmp = (180.0 * t_0) / pi;
	elseif (A <= 1.45e+78)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -2.8e-95], N[(N[(180.0 * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.12e-126], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -5.5e-193], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.05e-294], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.45e+78], 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 / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -2.7999999999999999e-95

   1. Initial program 34.2%

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

      1. associate-*r/ 34.2%

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

      2. associate-*l/ 34.2%

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

      3. *-un-lft-identity 34.2%

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

      4. unpow2 34.2%

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

      5. unpow2 34.2%

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

      6. hypot-define 58.6%

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

   4. Applied egg-rr 58.6%

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

   5. Taylor expanded in A around -inf 59.4%

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

      1. associate-*r/ 59.4%

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

      2. *-commutative 59.4%

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

      3. associate-*r/ 59.4%

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

   7. Simplified 59.4%

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

   if -2.7999999999999999e-95 < A < -1.12e-126

   1. Initial program 44.0%

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

   3. Taylor expanded in A around 0 44.0%

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

      1. unpow2 44.0%

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

      2. unpow2 44.0%

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

      3. hypot-define 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in C around inf 60.5%

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

   if -1.12e-126 < A < -5.50000000000000014e-193

   1. Initial program 65.3%

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

   3. Taylor expanded in B around -inf 49.7%

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

   if -5.50000000000000014e-193 < A < 2.0499999999999999e-294

   1. Initial program 43.6%

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

      1. associate-*r/ 43.6%

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

      2. associate-*l/ 43.6%

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

      3. *-un-lft-identity 43.6%

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

      4. unpow2 43.6%

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

      5. unpow2 43.6%

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

      6. hypot-define 58.0%

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

   4. Applied egg-rr 58.0%

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

   5. Taylor expanded in A around 0 43.6%

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

      1. unpow2 43.6%

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

      2. unpow2 43.6%

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

      3. hypot-undefine 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in C around inf 52.6%

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

   if 2.0499999999999999e-294 < A < 1.45000000000000008e78

   1. Initial program 55.5%

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

   3. Taylor expanded in A around 0 46.1%

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

      1. unpow2 46.1%

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

      2. unpow2 46.1%

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

      3. hypot-define 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in C around 0 54.9%

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

   if 1.45000000000000008e78 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in A around inf 76.8%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.12 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-294}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;A \leq -1.3 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B C)))))
   (if (<= A -1.3e-93)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A -1.35e-126)
       (* 180.0 (/ t_0 PI))
       (if (<= A -5.1e-197)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= A 1.2e-300)
           (/ (* 180.0 t_0) PI)
           (if (<= A 3.4e+76)
             (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / C)));
	double tmp;
	if (A <= -1.3e-93) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -1.35e-126) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -5.1e-197) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.2e-300) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else if (A <= 3.4e+76) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / C)));
	double tmp;
	if (A <= -1.3e-93) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -1.35e-126) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -5.1e-197) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.2e-300) {
		tmp = (180.0 * t_0) / Math.PI;
	} else if (A <= 3.4e+76) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / C)))
	tmp = 0
	if A <= -1.3e-93:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -1.35e-126:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -5.1e-197:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.2e-300:
		tmp = (180.0 * t_0) / math.pi
	elif A <= 3.4e+76:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / C)))
	tmp = 0.0
	if (A <= -1.3e-93)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -1.35e-126)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -5.1e-197)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.2e-300)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	elseif (A <= 3.4e+76)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (A <= -1.3e-93)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -1.35e-126)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -5.1e-197)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.2e-300)
		tmp = (180.0 * t_0) / pi;
	elseif (A <= 3.4e+76)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.3e-93], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.35e-126], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -5.1e-197], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.2e-300], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.4e+76], 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 / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -1.2999999999999999e-93

   1. Initial program 34.2%

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

   3. Taylor expanded in A around -inf 59.3%

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

      1. associate-*r/ 59.3%

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

   5. Simplified 59.3%

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

   if -1.2999999999999999e-93 < A < -1.34999999999999998e-126

   1. Initial program 44.0%

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

   3. Taylor expanded in A around 0 44.0%

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

      1. unpow2 44.0%

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

      2. unpow2 44.0%

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

      3. hypot-define 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in C around inf 60.5%

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

   if -1.34999999999999998e-126 < A < -5.1000000000000003e-197

   1. Initial program 65.3%

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

   3. Taylor expanded in B around -inf 49.7%

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

   if -5.1000000000000003e-197 < A < 1.2e-300

   1. Initial program 43.6%

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

      1. associate-*r/ 43.6%

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

      2. associate-*l/ 43.6%

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

      3. *-un-lft-identity 43.6%

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

      4. unpow2 43.6%

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

      5. unpow2 43.6%

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

      6. hypot-define 58.0%

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

   4. Applied egg-rr 58.0%

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

   5. Taylor expanded in A around 0 43.6%

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

      1. unpow2 43.6%

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

      2. unpow2 43.6%

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

      3. hypot-undefine 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in C around inf 52.6%

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

   if 1.2e-300 < A < 3.3999999999999997e76

   1. Initial program 55.5%

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

   3. Taylor expanded in A around 0 46.1%

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

      1. unpow2 46.1%

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

      2. unpow2 46.1%

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

      3. hypot-define 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in C around 0 54.9%

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

   if 3.3999999999999997e76 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in A around inf 76.8%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-127}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-300}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= A -3.7e-91)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A -8.5e-127)
       t_0
       (if (<= A -8.8e-194)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= A 1.4e-300)
           t_0
           (if (<= A 1.45e+78)
             (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (A <= -3.7e-91) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -8.5e-127) {
		tmp = t_0;
	} else if (A <= -8.8e-194) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.4e-300) {
		tmp = t_0;
	} else if (A <= 1.45e+78) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (A <= -3.7e-91) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -8.5e-127) {
		tmp = t_0;
	} else if (A <= -8.8e-194) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.4e-300) {
		tmp = t_0;
	} else if (A <= 1.45e+78) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if A <= -3.7e-91:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -8.5e-127:
		tmp = t_0
	elif A <= -8.8e-194:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.4e-300:
		tmp = t_0
	elif A <= 1.45e+78:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (A <= -3.7e-91)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -8.5e-127)
		tmp = t_0;
	elseif (A <= -8.8e-194)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.4e-300)
		tmp = t_0;
	elseif (A <= 1.45e+78)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (A <= -3.7e-91)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -8.5e-127)
		tmp = t_0;
	elseif (A <= -8.8e-194)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.4e-300)
		tmp = t_0;
	elseif (A <= 1.45e+78)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.7e-91], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.5e-127], t$95$0, If[LessEqual[A, -8.8e-194], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4e-300], t$95$0, If[LessEqual[A, 1.45e+78], 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 / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -3.7000000000000002e-91

   1. Initial program 34.2%

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

   3. Taylor expanded in A around -inf 59.3%

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

      1. associate-*r/ 59.3%

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

   5. Simplified 59.3%

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

   if -3.7000000000000002e-91 < A < -8.5e-127 or -8.8000000000000005e-194 < A < 1.39999999999999997e-300

   1. Initial program 43.8%

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

   3. Taylor expanded in A around 0 43.8%

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

      1. unpow2 43.8%

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

      2. unpow2 43.8%

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

      3. hypot-define 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in C around inf 55.7%

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

   if -8.5e-127 < A < -8.8000000000000005e-194

   1. Initial program 65.3%

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

   3. Taylor expanded in B around -inf 49.7%

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

   if 1.39999999999999997e-300 < A < 1.45000000000000008e78

   1. Initial program 55.5%

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

   3. Taylor expanded in A around 0 46.1%

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

      1. unpow2 46.1%

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

      2. unpow2 46.1%

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

      3. hypot-define 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in C around 0 54.9%

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

   if 1.45000000000000008e78 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in A around inf 76.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;C \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1.15 \cdot 10^{-234}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.68 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-235}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= C -2.6e-20)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -4.8e-87)
       t_0
       (if (<= C -1.15e-234)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= C 1.68e-295)
           (* 180.0 (/ (atan 1.0) PI))
           (if (<= C 1.95e-235)
             t_0
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (C <= -2.6e-20) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -4.8e-87) {
		tmp = t_0;
	} else if (C <= -1.15e-234) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 1.68e-295) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 1.95e-235) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (C <= -2.6e-20) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -4.8e-87) {
		tmp = t_0;
	} else if (C <= -1.15e-234) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 1.68e-295) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 1.95e-235) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if C <= -2.6e-20:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -4.8e-87:
		tmp = t_0
	elif C <= -1.15e-234:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 1.68e-295:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 1.95e-235:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (C <= -2.6e-20)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -4.8e-87)
		tmp = t_0;
	elseif (C <= -1.15e-234)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 1.68e-295)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 1.95e-235)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (C <= -2.6e-20)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -4.8e-87)
		tmp = t_0;
	elseif (C <= -1.15e-234)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 1.68e-295)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 1.95e-235)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -2.6e-20], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -4.8e-87], t$95$0, If[LessEqual[C, -1.15e-234], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.68e-295], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.95e-235], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -2.59999999999999995e-20

   1. Initial program 79.9%

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

   3. Taylor expanded in C around -inf 71.9%

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

   if -2.59999999999999995e-20 < C < -4.7999999999999999e-87 or 1.6799999999999999e-295 < C < 1.94999999999999985e-235

   1. Initial program 48.5%

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

   3. Taylor expanded in B around inf 44.8%

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

   if -4.7999999999999999e-87 < C < -1.14999999999999995e-234

   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 inf 43.4%

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

   if -1.14999999999999995e-234 < C < 1.6799999999999999e-295

   1. Initial program 40.6%

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

   3. Taylor expanded in B around -inf 54.6%

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

   if 1.94999999999999985e-235 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in A around 0 21.5%

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

      1. unpow2 21.5%

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

      2. unpow2 21.5%

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

      3. hypot-define 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in C around inf 53.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -1.15 \cdot 10^{-234}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.68 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;C \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.1 \cdot 10^{-86}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -6.1 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-235}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= C -1.65e-19)
     (/ (* 180.0 (atan (/ C B))) PI)
     (if (<= C -1.1e-86)
       t_0
       (if (<= C -6.1e-235)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= C 1.85e-295)
           (* 180.0 (/ (atan 1.0) PI))
           (if (<= C 2.3e-235)
             t_0
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (C <= -1.65e-19) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (C <= -1.1e-86) {
		tmp = t_0;
	} else if (C <= -6.1e-235) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 1.85e-295) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 2.3e-235) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (C <= -1.65e-19) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (C <= -1.1e-86) {
		tmp = t_0;
	} else if (C <= -6.1e-235) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 1.85e-295) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 2.3e-235) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if C <= -1.65e-19:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif C <= -1.1e-86:
		tmp = t_0
	elif C <= -6.1e-235:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 1.85e-295:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 2.3e-235:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (C <= -1.65e-19)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (C <= -1.1e-86)
		tmp = t_0;
	elseif (C <= -6.1e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 1.85e-295)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 2.3e-235)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (C <= -1.65e-19)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (C <= -1.1e-86)
		tmp = t_0;
	elseif (C <= -6.1e-235)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 1.85e-295)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 2.3e-235)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.65e-19], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, -1.1e-86], t$95$0, If[LessEqual[C, -6.1e-235], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e-295], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.3e-235], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.6499999999999999e-19

   1. Initial program 79.9%

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

      1. associate-*r/ 79.9%

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

      2. associate-*l/ 79.9%

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

      3. *-un-lft-identity 79.9%

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

      4. unpow2 79.9%

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

      5. unpow2 79.9%

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

      6. hypot-define 93.8%

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

   4. Applied egg-rr 93.8%

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

   5. Taylor expanded in A around 0 78.6%

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

      1. unpow2 78.6%

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

      2. unpow2 78.6%

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

      3. hypot-undefine 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in C around 0 76.8%

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

   9. Taylor expanded in C around inf 71.4%

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

   if -1.6499999999999999e-19 < C < -1.1000000000000001e-86 or 1.85e-295 < C < 2.29999999999999997e-235

   1. Initial program 48.5%

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

   3. Taylor expanded in B around inf 44.8%

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

   if -1.1000000000000001e-86 < C < -6.09999999999999988e-235

   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 inf 43.4%

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

   if -6.09999999999999988e-235 < C < 1.85e-295

   1. Initial program 40.6%

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

   3. Taylor expanded in B around -inf 54.6%

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

   if 2.29999999999999997e-235 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in A around 0 21.5%

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

      1. unpow2 21.5%

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

      2. unpow2 21.5%

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

      3. hypot-define 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in C around inf 53.8%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.1 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -6.1 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.42 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-175}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 450000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -1.42e+19)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1.6e-106)
       t_0
       (if (<= B 7.6e-180)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 1.2e-175)
           t_0
           (if (<= B 450000.0)
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((C / B))) / ((double) M_PI);
	double tmp;
	if (B <= -1.42e+19) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.6e-106) {
		tmp = t_0;
	} else if (B <= 7.6e-180) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.2e-175) {
		tmp = t_0;
	} else if (B <= 450000.0) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((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 t_0 = (180.0 * Math.atan((C / B))) / Math.PI;
	double tmp;
	if (B <= -1.42e+19) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.6e-106) {
		tmp = t_0;
	} else if (B <= 7.6e-180) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.2e-175) {
		tmp = t_0;
	} else if (B <= 450000.0) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((C / B))) / math.pi
	tmp = 0
	if B <= -1.42e+19:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.6e-106:
		tmp = t_0
	elif B <= 7.6e-180:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.2e-175:
		tmp = t_0
	elif B <= 450000.0:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(C / B))) / pi)
	tmp = 0.0
	if (B <= -1.42e+19)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.6e-106)
		tmp = t_0;
	elseif (B <= 7.6e-180)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.2e-175)
		tmp = t_0;
	elseif (B <= 450000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((C / B))) / pi;
	tmp = 0.0;
	if (B <= -1.42e+19)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.6e-106)
		tmp = t_0;
	elseif (B <= 7.6e-180)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.2e-175)
		tmp = t_0;
	elseif (B <= 450000.0)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -1.42e+19], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.6e-106], t$95$0, If[LessEqual[B, 7.6e-180], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.2e-175], t$95$0, If[LessEqual[B, 450000.0], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.42e19

   1. Initial program 48.3%

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

   3. Taylor expanded in B around -inf 68.3%

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

   if -1.42e19 < B < -1.6e-106 or 7.59999999999999999e-180 < B < 1.2e-175

   1. Initial program 63.3%

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

      1. associate-*r/ 63.2%

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

      2. associate-*l/ 63.2%

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

      3. *-un-lft-identity 63.2%

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

      4. unpow2 63.2%

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

      5. unpow2 63.2%

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

      6. hypot-define 69.3%

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

   4. Applied egg-rr 69.3%

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

   5. Taylor expanded in A around 0 53.5%

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

      1. unpow2 53.5%

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

      2. unpow2 53.5%

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

      3. hypot-undefine 59.2%

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

   7. Simplified 59.2%

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

   8. Taylor expanded in C around 0 45.4%

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

   9. Taylor expanded in C around inf 46.1%

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

   if -1.6e-106 < B < 7.59999999999999999e-180

   1. Initial program 53.0%

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

   3. Taylor expanded in C around inf 35.7%

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

      1. associate-*r/ 35.7%

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

      2. distribute-rgt1-in 35.7%

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

      3. metadata-eval 35.7%

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

      4. mul0-lft 35.7%

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

      5. metadata-eval 35.7%

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

   5. Simplified 35.7%

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

   if 1.2e-175 < B < 4.5e5

   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. Taylor expanded in A around inf 42.3%

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

   if 4.5e5 < B

   1. Initial program 42.7%

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

   3. Taylor expanded in B around inf 59.7%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.42 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 450000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.05 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.8e-122)
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
   (if (<= C -3.05e-235)
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
     (if (<= C 1.95e-295)
       (* 180.0 (/ (atan 1.0) PI))
       (if (<= C 2.5e-235)
         (* 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 <= -1.8e-122) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= -3.05e-235) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 1.95e-295) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 2.5e-235) {
		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 <= -1.8e-122) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else if (C <= -3.05e-235) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 1.95e-295) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 2.5e-235) {
		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 <= -1.8e-122:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	elif C <= -3.05e-235:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 1.95e-295:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 2.5e-235:
		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 <= -1.8e-122)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	elseif (C <= -3.05e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 1.95e-295)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 2.5e-235)
		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 <= -1.8e-122)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	elseif (C <= -3.05e-235)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 1.95e-295)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 2.5e-235)
		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, -1.8e-122], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.05e-235], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.95e-295], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.5e-235], 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 5 regimes

2. if C < -1.79999999999999997e-122

   1. Initial program 72.8%

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

   3. Taylor expanded in A around 0 69.1%

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

      1. unpow2 69.1%

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

      2. unpow2 69.1%

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

      3. hypot-define 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in C around 0 69.5%

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

   if -1.79999999999999997e-122 < C < -3.04999999999999994e-235

   1. Initial program 68.6%

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

   3. Taylor expanded in A around inf 45.0%

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

   if -3.04999999999999994e-235 < C < 1.95e-295

   1. Initial program 40.6%

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

   3. Taylor expanded in B around -inf 54.6%

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

   if 1.95e-295 < C < 2.4999999999999999e-235

   1. Initial program 61.8%

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

   3. Taylor expanded in B around inf 46.4%

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

   if 2.4999999999999999e-235 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in A around 0 21.5%

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

      1. unpow2 21.5%

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

      2. unpow2 21.5%

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

      3. hypot-define 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in C around inf 53.8%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.05 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -7 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 5.7 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-114}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -7e+16)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -9.5e-107)
       t_0
       (if (<= B 5.7e-180)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 8e-114) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((C / B))) / ((double) M_PI);
	double tmp;
	if (B <= -7e+16) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.5e-107) {
		tmp = t_0;
	} else if (B <= 5.7e-180) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 8e-114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((C / B))) / Math.PI;
	double tmp;
	if (B <= -7e+16) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.5e-107) {
		tmp = t_0;
	} else if (B <= 5.7e-180) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 8e-114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((C / B))) / math.pi
	tmp = 0
	if B <= -7e+16:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.5e-107:
		tmp = t_0
	elif B <= 5.7e-180:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 8e-114:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(C / B))) / pi)
	tmp = 0.0
	if (B <= -7e+16)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.5e-107)
		tmp = t_0;
	elseif (B <= 5.7e-180)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 8e-114)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((C / B))) / pi;
	tmp = 0.0;
	if (B <= -7e+16)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.5e-107)
		tmp = t_0;
	elseif (B <= 5.7e-180)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 8e-114)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -7e+16], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-107], t$95$0, If[LessEqual[B, 5.7e-180], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8e-114], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7e16

   1. Initial program 48.3%

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

   3. Taylor expanded in B around -inf 68.3%

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

   if -7e16 < B < -9.4999999999999999e-107 or 5.69999999999999977e-180 < B < 8.0000000000000004e-114

   1. Initial program 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*l/ 66.7%

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

      3. *-un-lft-identity 66.7%

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

      4. unpow2 66.7%

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

      5. unpow2 66.7%

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

      6. hypot-define 71.2%

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

   4. Applied egg-rr 71.2%

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

   5. Taylor expanded in A around 0 53.2%

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

      1. unpow2 53.2%

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

      2. unpow2 53.2%

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

      3. hypot-undefine 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in C around 0 45.1%

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

   9. Taylor expanded in C around inf 45.4%

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

   if -9.4999999999999999e-107 < B < 5.69999999999999977e-180

   1. Initial program 53.0%

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

   3. Taylor expanded in C around inf 35.7%

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

      1. associate-*r/ 35.7%

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

      2. distribute-rgt1-in 35.7%

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

      3. metadata-eval 35.7%

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

      4. mul0-lft 35.7%

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

      5. metadata-eval 35.7%

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

   5. Simplified 35.7%

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

   if 8.0000000000000004e-114 < B

   1. Initial program 47.0%

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

   3. Taylor expanded in B around inf 48.2%

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

Alternative 16: 60.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -7.5 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A}{B} + \left(-1 - \frac{C}{B}\right)}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{-76}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= C -7.5e-56)
     t_0
     (if (<= C -1.7e-86)
       (/ (* 180.0 (atan (/ 1.0 (+ (/ A B) (- -1.0 (/ C B)))))) PI)
       (if (<= C 8.6e-76) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (C <= -7.5e-56) {
		tmp = t_0;
	} else if (C <= -1.7e-86) {
		tmp = (180.0 * atan((1.0 / ((A / B) + (-1.0 - (C / B)))))) / ((double) M_PI);
	} else if (C <= 8.6e-76) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (C <= -7.5e-56) {
		tmp = t_0;
	} else if (C <= -1.7e-86) {
		tmp = (180.0 * Math.atan((1.0 / ((A / B) + (-1.0 - (C / B)))))) / Math.PI;
	} else if (C <= 8.6e-76) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if C <= -7.5e-56:
		tmp = t_0
	elif C <= -1.7e-86:
		tmp = (180.0 * math.atan((1.0 / ((A / B) + (-1.0 - (C / B)))))) / math.pi
	elif C <= 8.6e-76:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (C <= -7.5e-56)
		tmp = t_0;
	elseif (C <= -1.7e-86)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(A / B) + Float64(-1.0 - Float64(C / B)))))) / pi);
	elseif (C <= 8.6e-76)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (C <= -7.5e-56)
		tmp = t_0;
	elseif (C <= -1.7e-86)
		tmp = (180.0 * atan((1.0 / ((A / B) + (-1.0 - (C / B)))))) / pi;
	elseif (C <= 8.6e-76)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7.5e-56], t$95$0, If[LessEqual[C, -1.7e-86], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(A / B), $MachinePrecision] + N[(-1.0 - N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 8.6e-76], t$95$0, 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 < -7.50000000000000041e-56 or -1.7e-86 < C < 8.5999999999999998e-76

   1. Initial program 67.9%

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

   3. Taylor expanded in B around -inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. div-sub 66.1%

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

   5. Simplified 66.1%

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

   if -7.50000000000000041e-56 < C < -1.7e-86

   1. Initial program 40.6%

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

      1. associate-*r/ 40.6%

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

      2. associate-*l/ 40.6%

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

      3. *-un-lft-identity 40.6%

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

      4. unpow2 40.6%

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

      5. unpow2 40.6%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. associate--l- 51.6%

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

   6. Applied egg-rr 51.6%

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

      1. unpow-1 51.6%

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

   8. Simplified 51.6%

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

   9. Taylor expanded in B around inf 100.0%

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

   if 8.5999999999999998e-76 < C

   1. Initial program 20.6%

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

   3. Taylor expanded in A around 0 15.0%

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

      1. unpow2 15.0%

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

      2. unpow2 15.0%

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

      3. hypot-define 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in C around inf 65.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.5 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{A}{B} + \left(-1 - \frac{C}{B}\right)}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-206}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= C -3.4e+25)
     t_0
     (if (<= C -1e-206)
       (/ (* 180.0 (atan (+ (/ C B) (- -1.0 (/ A B))))) PI)
       (if (<= C 8.2e-75) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (C <= -3.4e+25) {
		tmp = t_0;
	} else if (C <= -1e-206) {
		tmp = (180.0 * atan(((C / B) + (-1.0 - (A / B))))) / ((double) M_PI);
	} else if (C <= 8.2e-75) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (C <= -3.4e+25) {
		tmp = t_0;
	} else if (C <= -1e-206) {
		tmp = (180.0 * Math.atan(((C / B) + (-1.0 - (A / B))))) / Math.PI;
	} else if (C <= 8.2e-75) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if C <= -3.4e+25:
		tmp = t_0
	elif C <= -1e-206:
		tmp = (180.0 * math.atan(((C / B) + (-1.0 - (A / B))))) / math.pi
	elif C <= 8.2e-75:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (C <= -3.4e+25)
		tmp = t_0;
	elseif (C <= -1e-206)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B))))) / pi);
	elseif (C <= 8.2e-75)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (C <= -3.4e+25)
		tmp = t_0;
	elseif (C <= -1e-206)
		tmp = (180.0 * atan(((C / B) + (-1.0 - (A / B))))) / pi;
	elseif (C <= 8.2e-75)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -3.4e+25], t$95$0, If[LessEqual[C, -1e-206], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 8.2e-75], t$95$0, 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 < -3.39999999999999984e25 or -1.00000000000000003e-206 < C < 8.20000000000000005e-75

   1. Initial program 68.6%

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

   3. Taylor expanded in B around -inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. div-sub 70.1%

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

   5. Simplified 70.1%

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

   if -3.39999999999999984e25 < C < -1.00000000000000003e-206

   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. Step-by-step derivation

      1. associate-*r/ 62.4%

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

      2. associate-*l/ 62.4%

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

      3. *-un-lft-identity 62.4%

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

      4. unpow2 62.4%

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

      5. unpow2 62.4%

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

      6. hypot-define 85.2%

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

   4. Applied egg-rr 85.2%

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

   5. Taylor expanded in B around inf 57.9%

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

   if 8.20000000000000005e-75 < C

   1. Initial program 20.6%

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

   3. Taylor expanded in A around 0 15.0%

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

      1. unpow2 15.0%

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

      2. unpow2 15.0%

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

      3. hypot-define 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in C around inf 65.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-206}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 61.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -2.7 \cdot 10^{-206}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= C -3.4e+25)
     t_0
     (if (<= C -2.7e-206)
       (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))
       (if (<= C 4.1e-72) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (C <= -3.4e+25) {
		tmp = t_0;
	} else if (C <= -2.7e-206) {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	} else if (C <= 4.1e-72) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (C <= -3.4e+25) {
		tmp = t_0;
	} else if (C <= -2.7e-206) {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	} else if (C <= 4.1e-72) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if C <= -3.4e+25:
		tmp = t_0
	elif C <= -2.7e-206:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	elif C <= 4.1e-72:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (C <= -3.4e+25)
		tmp = t_0;
	elseif (C <= -2.7e-206)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	elseif (C <= 4.1e-72)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (C <= -3.4e+25)
		tmp = t_0;
	elseif (C <= -2.7e-206)
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	elseif (C <= 4.1e-72)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -3.4e+25], t$95$0, If[LessEqual[C, -2.7e-206], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.1e-72], t$95$0, 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 < -3.39999999999999984e25 or -2.7000000000000001e-206 < C < 4.10000000000000003e-72

   1. Initial program 68.6%

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

   3. Taylor expanded in B around -inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. div-sub 70.1%

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

   5. Simplified 70.1%

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

   if -3.39999999999999984e25 < C < -2.7000000000000001e-206

   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 B around inf 57.9%

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

   if 4.10000000000000003e-72 < C

   1. Initial program 20.6%

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

   3. Taylor expanded in A around 0 15.0%

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

      1. unpow2 15.0%

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

      2. unpow2 15.0%

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

      3. hypot-define 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in C around inf 65.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.7 \cdot 10^{-206}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-58)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7.8e-180)
     (* 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 <= -2.1e-58) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.8e-180) {
		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 <= -2.1e-58) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.8e-180) {
		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 <= -2.1e-58:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.8e-180:
		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 <= -2.1e-58)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.8e-180)
		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 <= -2.1e-58)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.8e-180)
		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, -2.1e-58], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.8e-180], 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 < -2.09999999999999988e-58

   1. Initial program 55.3%

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

   3. Taylor expanded in B around -inf 55.5%

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

   if -2.09999999999999988e-58 < B < 7.8000000000000005e-180

   1. Initial program 50.4%

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

   3. Taylor expanded in C around inf 34.3%

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

      1. associate-*r/ 34.3%

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

      2. distribute-rgt1-in 34.3%

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

      3. metadata-eval 34.3%

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

      4. mul0-lft 34.3%

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

      5. metadata-eval 34.3%

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

   5. Simplified 34.3%

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

   if 7.8000000000000005e-180 < B

   1. Initial program 51.8%

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

   3. Taylor expanded in B around inf 43.5%

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

Alternative 20: 61.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 5.6e-78)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 5.6e-78) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((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 <= 5.6e-78) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / 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 <= 5.6e-78:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / 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 <= 5.6e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / 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 <= 5.6e-78)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 5.6e-78], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $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 2 regimes

2. if C < 5.60000000000000047e-78

   1. Initial program 67.0%

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

   3. Taylor expanded in B around -inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. div-sub 63.9%

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

   5. Simplified 63.9%

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

   if 5.60000000000000047e-78 < C

   1. Initial program 20.6%

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

   3. Taylor expanded in A around 0 15.0%

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

      1. unpow2 15.0%

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

      2. unpow2 15.0%

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

      3. hypot-define 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in C around inf 65.7%

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

Alternative 21: 39.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.95 \cdot 10^{-298}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.95e-298)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.95e-298) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.95e-298) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.95e-298:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.95e-298)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.95e-298)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.95e-298], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -2.94999999999999984e-298

   1. Initial program 50.7%

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

   3. Taylor expanded in B around -inf 40.3%

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

   if -2.94999999999999984e-298 < B

   1. Initial program 54.0%

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

   3. Taylor expanded in B around inf 34.2%

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

Alternative 22: 21.2% 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 52.5%

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

3. Taylor expanded in B around inf 18.8%

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

Reproduce

herbie shell --seed 2024091 
(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)))