ABCF->ab-angle angle

Percentage Accurate: 53.7% → 82.6%

Time: 29.6s

Alternatives: 22

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% 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: 82.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.8e+50)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e+50) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e+50) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.8e+50:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.8e+50)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.8e+50)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.8e+50], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.7999999999999997e50

   1. Initial program 17.0%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in B around 0 80.4%

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

      1. associate-*r/ 80.4%

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

   6. Simplified 80.4%

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

   if -6.7999999999999997e50 < A

   1. Initial program 67.7%

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

   3. Simplified 84.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 2: 82.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.24 \cdot 10^{+51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.24e+51)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.24e+51) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} 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 <= -1.24e+51) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} 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 <= -1.24e+51:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	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 <= -1.24e+51)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	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 <= -1.24e+51)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	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, -1.24e+51], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $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 < -1.24000000000000001e51

   1. Initial program 17.0%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in B around 0 80.4%

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

      1. associate-*r/ 80.4%

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

   6. Simplified 80.4%

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

   if -1.24000000000000001e51 < A

   1. Initial program 67.7%

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

   3. Simplified 84.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.24 \cdot 10^{+51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 76.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.3e+50)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (if (<= A 1.7e-8)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.3e+50) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else if (A <= 1.7e-8) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.3e+50) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else if (A <= 1.7e-8) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.3e+50:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	elif A <= 1.7e-8:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.3e+50)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	elseif (A <= 1.7e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.3e+50)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	elseif (A <= 1.7e-8)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.3e+50], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.7e-8], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.3000000000000003e50

   1. Initial program 17.0%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in B around 0 80.4%

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

      1. associate-*r/ 80.4%

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

   6. Simplified 80.4%

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

   if -7.3000000000000003e50 < A < 1.7e-8

   1. Initial program 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in A around 0 59.2%

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

      1. unpow2 59.2%

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

      2. unpow2 59.2%

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

      3. hypot-def 76.7%

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

   6. Simplified 76.7%

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

   if 1.7e-8 < A

   1. Initial program 80.1%

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

      1. associate-*r/ 80.2%

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

      2. associate-*l/ 80.2%

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

      3. *-un-lft-identity 80.2%

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

      4. associate--l- 80.2%

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

      5. unpow2 80.2%

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

      6. pow2 80.2%

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

      7. hypot-def 96.7%

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

   3. Applied egg-rr 96.7%

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

   4. Taylor expanded in B around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in C around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. remove-double-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. div-sub 85.6%

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

      5. *-inverses 85.6%

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

      6. neg-mul-1 85.6%

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

      7. associate-*r/ 85.6%

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

      8. cancel-sign-sub-inv 85.6%

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

      9. metadata-eval 85.6%

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

      10. *-lft-identity 85.6%

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

      11. distribute-lft-in 85.6%

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

      12. metadata-eval 85.6%

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

      13. mul-1-neg 85.6%

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

      14. unsub-neg 85.6%

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

   9. Simplified 85.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 79.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.4e+50)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (if (<= A 6e-38)
     (* 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 <= -7.4e+50) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else if (A <= 6e-38) {
		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 <= -7.4e+50) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else if (A <= 6e-38) {
		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 <= -7.4e+50:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	elif A <= 6e-38:
		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 <= -7.4e+50)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	elseif (A <= 6e-38)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(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 <= -7.4e+50)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	elseif (A <= 6e-38)
		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, -7.4e+50], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-38], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.4000000000000001e50

   1. Initial program 17.0%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in B around 0 80.4%

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

      1. associate-*r/ 80.4%

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

   6. Simplified 80.4%

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

   if -7.4000000000000001e50 < A < 5.99999999999999977e-38

   1. Initial program 60.6%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in A around 0 59.2%

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

      1. unpow2 59.2%

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

      2. unpow2 59.2%

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

      3. hypot-def 77.4%

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

   6. Simplified 77.4%

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

   if 5.99999999999999977e-38 < A

   1. Initial program 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in C around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. mul-1-neg 78.5%

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

      3. +-commutative 78.5%

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

      4. unpow2 78.5%

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

      5. unpow2 78.5%

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

      6. hypot-def 92.2%

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

   6. Simplified 92.2%

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

      1. expm1-log1p-u 42.2%

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

      2. expm1-udef 42.2%

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

      3. associate-*r/ 42.2%

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

      4. distribute-frac-neg 42.2%

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

      5. atan-neg 42.2%

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

   8. Applied egg-rr 42.2%

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

      1. expm1-def 42.2%

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

      2. expm1-log1p 92.2%

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

      3. distribute-rgt-neg-out 92.2%

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

      4. distribute-lft-neg-in 92.2%

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

      5. metadata-eval 92.2%

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

   10. Simplified 92.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 54.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;C \leq -1.42 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 9.8 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;C \leq 2700:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))
        (t_1 (* (/ 180.0 PI) (atan (* 0.5 (/ B A)))))
        (t_2 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= C -1.42e-32)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -1.65e-304)
       t_0
       (if (<= C 4.2e-287)
         t_1
         (if (<= C 7e-269)
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
           (if (<= C 4.2e-247)
             t_2
             (if (<= C 1.5e-242)
               t_1
               (if (<= C 1.05e-75)
                 t_0
                 (if (<= C 9.8e-26)
                   t_2
                   (if (<= C 2700.0)
                     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 - (A / B))) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	double t_2 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (C <= -1.42e-32) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -1.65e-304) {
		tmp = t_0;
	} else if (C <= 4.2e-287) {
		tmp = t_1;
	} else if (C <= 7e-269) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (C <= 4.2e-247) {
		tmp = t_2;
	} else if (C <= 1.5e-242) {
		tmp = t_1;
	} else if (C <= 1.05e-75) {
		tmp = t_0;
	} else if (C <= 9.8e-26) {
		tmp = t_2;
	} else if (C <= 2700.0) {
		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 - (A / B))) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	double t_2 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (C <= -1.42e-32) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -1.65e-304) {
		tmp = t_0;
	} else if (C <= 4.2e-287) {
		tmp = t_1;
	} else if (C <= 7e-269) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (C <= 4.2e-247) {
		tmp = t_2;
	} else if (C <= 1.5e-242) {
		tmp = t_1;
	} else if (C <= 1.05e-75) {
		tmp = t_0;
	} else if (C <= 9.8e-26) {
		tmp = t_2;
	} else if (C <= 2700.0) {
		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 - (A / B))) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	t_2 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if C <= -1.42e-32:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -1.65e-304:
		tmp = t_0
	elif C <= 4.2e-287:
		tmp = t_1
	elif C <= 7e-269:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif C <= 4.2e-247:
		tmp = t_2
	elif C <= 1.5e-242:
		tmp = t_1
	elif C <= 1.05e-75:
		tmp = t_0
	elif C <= 9.8e-26:
		tmp = t_2
	elif C <= 2700.0:
		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(A / B))) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))))
	t_2 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (C <= -1.42e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -1.65e-304)
		tmp = t_0;
	elseif (C <= 4.2e-287)
		tmp = t_1;
	elseif (C <= 7e-269)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (C <= 4.2e-247)
		tmp = t_2;
	elseif (C <= 1.5e-242)
		tmp = t_1;
	elseif (C <= 1.05e-75)
		tmp = t_0;
	elseif (C <= 9.8e-26)
		tmp = t_2;
	elseif (C <= 2700.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	t_1 = (180.0 / pi) * atan((0.5 * (B / A)));
	t_2 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (C <= -1.42e-32)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -1.65e-304)
		tmp = t_0;
	elseif (C <= 4.2e-287)
		tmp = t_1;
	elseif (C <= 7e-269)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (C <= 4.2e-247)
		tmp = t_2;
	elseif (C <= 1.5e-242)
		tmp = t_1;
	elseif (C <= 1.05e-75)
		tmp = t_0;
	elseif (C <= 9.8e-26)
		tmp = t_2;
	elseif (C <= 2700.0)
		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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.42e-32], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.65e-304], t$95$0, If[LessEqual[C, 4.2e-287], t$95$1, If[LessEqual[C, 7e-269], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.2e-247], t$95$2, If[LessEqual[C, 1.5e-242], t$95$1, If[LessEqual[C, 1.05e-75], t$95$0, If[LessEqual[C, 9.8e-26], t$95$2, If[LessEqual[C, 2700.0], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if C < -1.4199999999999999e-32

   1. Initial program 78.1%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in C around -inf 68.9%

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

   if -1.4199999999999999e-32 < C < -1.65000000000000006e-304 or 1.5e-242 < C < 1.0500000000000001e-75 or 9.7999999999999998e-26 < C < 2700

   1. Initial program 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in C around 0 64.8%

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

      1. associate-*r/ 64.8%

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

      2. mul-1-neg 64.8%

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

      3. +-commutative 64.8%

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

      4. unpow2 64.8%

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

      5. unpow2 64.8%

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

      6. hypot-def 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in B around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   9. Simplified 59.4%

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

   if -1.65000000000000006e-304 < C < 4.1999999999999998e-287 or 4.20000000000000027e-247 < C < 1.5e-242

   1. Initial program 26.1%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in A around -inf 66.9%

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

      1. associate-*r/ 66.9%

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

   6. Simplified 66.9%

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

      1. associate-*r/ 67.0%

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

      2. *-commutative 67.0%

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

   8. Applied egg-rr 67.0%

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

   9. Taylor expanded in B around 0 66.9%

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

       1. associate-*r/ 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r/ 67.0%

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

       4. associate-*l/ 67.3%

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

       5. *-commutative 67.3%

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

       6. *-commutative 67.3%

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

       7. associate-*r/ 67.3%

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

   11. Simplified 67.3%

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

   if 4.1999999999999998e-287 < C < 7.00000000000000038e-269

   1. Initial program 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in A around inf 75.1%

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

      1. associate-*r/ 75.1%

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

      2. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if 7.00000000000000038e-269 < C < 4.20000000000000027e-247 or 1.0500000000000001e-75 < C < 9.7999999999999998e-26

   1. Initial program 49.1%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in B around inf 63.3%

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

   if 2700 < C

   1. Initial program 21.0%

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

      1. associate-*r/ 21.0%

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

      2. associate-*l/ 21.0%

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

      3. *-un-lft-identity 21.0%

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

      4. associate--l- 20.9%

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

      5. unpow2 20.9%

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

      6. pow2 20.9%

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

      7. hypot-def 43.8%

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

   3. Applied egg-rr 43.8%

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

   4. Taylor expanded in A around 0 24.0%

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

      1. unpow2 24.0%

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

      2. unpow2 24.0%

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

      3. hypot-def 45.3%

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

   6. Simplified 45.3%

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

   7. Taylor expanded in C around inf 64.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.42 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 7 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.8 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 2700:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6: 58.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -0.076:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-215}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (+ B C) B))) PI)))
   (if (<= A -0.076)
     (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
     (if (<= A -1.2e-259)
       t_0
       (if (<= A -7.4e-278)
         (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)
         (if (<= A 1.65e-215)
           t_0
           (/ (* 180.0 (atan (/ (- (+ A B)) B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	double tmp;
	if (A <= -0.076) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= -1.2e-259) {
		tmp = t_0;
	} else if (A <= -7.4e-278) {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	} else if (A <= 1.65e-215) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-(A + B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	double tmp;
	if (A <= -0.076) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= -1.2e-259) {
		tmp = t_0;
	} else if (A <= -7.4e-278) {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	} else if (A <= 1.65e-215) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-(A + B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((B + C) / B))) / math.pi
	tmp = 0
	if A <= -0.076:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= -1.2e-259:
		tmp = t_0
	elif A <= -7.4e-278:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	elif A <= 1.65e-215:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-(A + B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi)
	tmp = 0.0
	if (A <= -0.076)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= -1.2e-259)
		tmp = t_0;
	elseif (A <= -7.4e-278)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	elseif (A <= 1.65e-215)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-Float64(A + B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((B + C) / B))) / pi;
	tmp = 0.0;
	if (A <= -0.076)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= -1.2e-259)
		tmp = t_0;
	elseif (A <= -7.4e-278)
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	elseif (A <= 1.65e-215)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-(A + B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[A, -0.076], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.2e-259], t$95$0, If[LessEqual[A, -7.4e-278], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.65e-215], t$95$0, N[(N[(180.0 * N[ArcTan[N[((-N[(A + B), $MachinePrecision]) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -0.0759999999999999981

   1. Initial program 20.3%

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

   3. Simplified 17.1%

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

   4. Taylor expanded in A around -inf 69.4%

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

      1. associate-*r/ 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in B around 0 69.4%

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

      1. associate-*r/ 69.5%

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

      2. associate-*r/ 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/l* 70.1%

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

      5. *-commutative 70.1%

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

      6. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

   if -0.0759999999999999981 < A < -1.2e-259 or -7.40000000000000045e-278 < A < 1.6499999999999999e-215

   1. Initial program 63.9%

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

      1. associate-*r/ 64.0%

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

      2. associate-*l/ 64.0%

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

      3. *-un-lft-identity 64.0%

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

      4. associate--l- 63.9%

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

      5. unpow2 63.9%

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

      6. pow2 63.9%

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

      7. hypot-def 83.0%

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

   3. Applied egg-rr 83.0%

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

   4. Taylor expanded in A around 0 63.5%

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

      1. unpow2 63.5%

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

      2. unpow2 63.5%

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

      3. hypot-def 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in B around -inf 57.1%

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

   if -1.2e-259 < A < -7.40000000000000045e-278

   1. Initial program 6.9%

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

      1. associate-*r/ 6.9%

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

      2. associate-*l/ 6.9%

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

      3. *-un-lft-identity 6.9%

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

      4. associate--l- 6.9%

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

      5. unpow2 6.9%

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

      6. pow2 6.9%

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

      7. hypot-def 24.0%

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

   3. Applied egg-rr 24.0%

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

   4. Taylor expanded in A around 0 6.9%

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

      1. unpow2 6.9%

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

      2. unpow2 6.9%

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

      3. hypot-def 24.0%

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

   6. Simplified 24.0%

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

   7. Taylor expanded in C around inf 83.4%

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

   if 1.6499999999999999e-215 < A

   1. Initial program 75.0%

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

      1. associate-*r/ 75.0%

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

      2. associate-*l/ 75.0%

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

      3. *-un-lft-identity 75.0%

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

      4. associate--l- 75.0%

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

      5. unpow2 75.0%

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

      6. pow2 75.0%

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

      7. hypot-def 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in B around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in C around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

      3. distribute-neg-in 70.3%

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

      4. sub-neg 70.3%

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

   9. Simplified 70.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.076:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-215}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-\left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 53.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.02 \cdot 10^{-287}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e-259)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A -1.02e-287)
     (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)
     (if (<= A 1.4e-302)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 2e-283)
         (* 180.0 (/ (atan 1.0) PI))
         (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-259) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= -1.02e-287) {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	} else if (A <= 1.4e-302) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 2e-283) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-259) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= -1.02e-287) {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	} else if (A <= 1.4e-302) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 2e-283) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e-259:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= -1.02e-287:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	elif A <= 1.4e-302:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 2e-283:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e-259)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= -1.02e-287)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	elseif (A <= 1.4e-302)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 2e-283)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e-259)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= -1.02e-287)
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	elseif (A <= 1.4e-302)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 2e-283)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e-259], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.02e-287], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.4e-302], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-283], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -4.19999999999999995e-259

   1. Initial program 40.6%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in A around -inf 56.4%

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

      1. associate-*r/ 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in B around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. associate-*r/ 56.4%

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

      3. *-commutative 56.4%

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

      4. associate-/l* 56.7%

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

      5. *-commutative 56.7%

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

      6. associate-*r/ 56.7%

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

   9. Simplified 56.7%

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

   if -4.19999999999999995e-259 < A < -1.01999999999999999e-287

   1. Initial program 29.1%

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

      1. associate-*r/ 29.1%

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

      2. associate-*l/ 29.1%

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

      3. *-un-lft-identity 29.1%

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

      4. associate--l- 29.1%

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

      5. unpow2 29.1%

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

      6. pow2 29.1%

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

      7. hypot-def 47.0%

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

   3. Applied egg-rr 47.0%

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

   4. Taylor expanded in A around 0 29.1%

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

      1. unpow2 29.1%

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

      2. unpow2 29.1%

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

      3. hypot-def 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in C around inf 59.9%

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

   if -1.01999999999999999e-287 < A < 1.4e-302

   1. Initial program 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in B around inf 60.5%

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

   if 1.4e-302 < A < 1.99999999999999989e-283

   1. Initial program 47.8%

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

   3. Simplified 47.8%

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

   4. Taylor expanded in B around -inf 60.6%

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

   if 1.99999999999999989e-283 < A

   1. Initial program 74.3%

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

      1. associate-*r/ 74.3%

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

      2. associate-*l/ 74.3%

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

      3. *-un-lft-identity 74.3%

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

      4. associate--l- 74.3%

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

      5. unpow2 74.3%

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

      6. pow2 74.3%

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

      7. hypot-def 90.0%

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

   3. Applied egg-rr 90.0%

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

   4. Taylor expanded in B around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in C around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. remove-double-neg 66.1%

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

      3. sub-neg 66.1%

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

      4. div-sub 66.1%

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

      5. *-inverses 66.1%

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

      6. neg-mul-1 66.1%

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

      7. associate-*r/ 66.1%

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

      8. cancel-sign-sub-inv 66.1%

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

      9. metadata-eval 66.1%

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

      10. *-lft-identity 66.1%

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

      11. distribute-lft-in 66.1%

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

      12. metadata-eval 66.1%

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

      13. mul-1-neg 66.1%

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

      14. unsub-neg 66.1%

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

   9. Simplified 66.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.02 \cdot 10^{-287}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -225:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.18 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (+ B C) B))) PI)))
   (if (<= A -225.0)
     (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
     (if (<= A -1.18e-259)
       t_0
       (if (<= A -5e-277)
         (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)
         (if (<= A 7e-210) t_0 (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	double tmp;
	if (A <= -225.0) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= -1.18e-259) {
		tmp = t_0;
	} else if (A <= -5e-277) {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	} else if (A <= 7e-210) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	double tmp;
	if (A <= -225.0) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= -1.18e-259) {
		tmp = t_0;
	} else if (A <= -5e-277) {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	} else if (A <= 7e-210) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((B + C) / B))) / math.pi
	tmp = 0
	if A <= -225.0:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= -1.18e-259:
		tmp = t_0
	elif A <= -5e-277:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	elif A <= 7e-210:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi)
	tmp = 0.0
	if (A <= -225.0)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= -1.18e-259)
		tmp = t_0;
	elseif (A <= -5e-277)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	elseif (A <= 7e-210)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((B + C) / B))) / pi;
	tmp = 0.0;
	if (A <= -225.0)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= -1.18e-259)
		tmp = t_0;
	elseif (A <= -5e-277)
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	elseif (A <= 7e-210)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[A, -225.0], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.18e-259], t$95$0, If[LessEqual[A, -5e-277], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 7e-210], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -225

   1. Initial program 20.3%

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

   3. Simplified 17.1%

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

   4. Taylor expanded in A around -inf 69.4%

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

      1. associate-*r/ 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in B around 0 69.4%

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

      1. associate-*r/ 69.5%

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

      2. associate-*r/ 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/l* 70.1%

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

      5. *-commutative 70.1%

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

      6. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

   if -225 < A < -1.18e-259 or -5e-277 < A < 7.00000000000000031e-210

   1. Initial program 63.9%

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

      1. associate-*r/ 64.0%

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

      2. associate-*l/ 64.0%

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

      3. *-un-lft-identity 64.0%

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

      4. associate--l- 63.9%

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

      5. unpow2 63.9%

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

      6. pow2 63.9%

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

      7. hypot-def 83.0%

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

   3. Applied egg-rr 83.0%

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

   4. Taylor expanded in A around 0 63.5%

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

      1. unpow2 63.5%

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

      2. unpow2 63.5%

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

      3. hypot-def 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in B around -inf 57.1%

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

   if -1.18e-259 < A < -5e-277

   1. Initial program 6.9%

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

      1. associate-*r/ 6.9%

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

      2. associate-*l/ 6.9%

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

      3. *-un-lft-identity 6.9%

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

      4. associate--l- 6.9%

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

      5. unpow2 6.9%

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

      6. pow2 6.9%

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

      7. hypot-def 24.0%

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

   3. Applied egg-rr 24.0%

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

   4. Taylor expanded in A around 0 6.9%

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

      1. unpow2 6.9%

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

      2. unpow2 6.9%

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

      3. hypot-def 24.0%

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

   6. Simplified 24.0%

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

   7. Taylor expanded in C around inf 83.4%

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

   if 7.00000000000000031e-210 < A

   1. Initial program 75.0%

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

      1. associate-*r/ 75.0%

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

      2. associate-*l/ 75.0%

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

      3. *-un-lft-identity 75.0%

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

      4. associate--l- 75.0%

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

      5. unpow2 75.0%

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

      6. pow2 75.0%

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

      7. hypot-def 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in B around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in C around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. remove-double-neg 70.3%

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

      3. sub-neg 70.3%

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

      4. div-sub 70.3%

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

      5. *-inverses 70.3%

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

      6. neg-mul-1 70.3%

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

      7. associate-*r/ 70.3%

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

      8. cancel-sign-sub-inv 70.3%

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

      9. metadata-eval 70.3%

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

      10. *-lft-identity 70.3%

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

      11. distribute-lft-in 70.3%

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

      12. metadata-eval 70.3%

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

      13. mul-1-neg 70.3%

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

      14. unsub-neg 70.3%

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

   9. Simplified 70.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -225:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.18 \cdot 10^{-259}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-210}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 62.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq 2.8 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-274}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B 2.8e-296)
     t_0
     (if (<= B 1.32e-274)
       (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
       (if (<= B 1.95e-122) t_0 (/ (* 180.0 (atan (- -1.0 (/ A B)))) 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 (B <= 2.8e-296) {
		tmp = t_0;
	} else if (B <= 1.32e-274) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (B <= 1.95e-122) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= 2.8e-296) {
		tmp = t_0;
	} else if (B <= 1.32e-274) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (B <= 1.95e-122) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= 2.8e-296:
		tmp = t_0
	elif B <= 1.32e-274:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif B <= 1.95e-122:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= 2.8e-296)
		tmp = t_0;
	elseif (B <= 1.32e-274)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (B <= 1.95e-122)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= 2.8e-296)
		tmp = t_0;
	elseif (B <= 1.32e-274)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (B <= 1.95e-122)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 2.8e-296], t$95$0, If[LessEqual[B, 1.32e-274], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-122], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < 2.7999999999999999e-296 or 1.32e-274 < B < 1.94999999999999995e-122

   1. Initial program 59.3%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around -inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. div-sub 65.0%

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

   6. Simplified 65.0%

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

   if 2.7999999999999999e-296 < B < 1.32e-274

   1. Initial program 45.1%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in A around -inf 81.9%

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

      1. associate-*r/ 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in B around 0 81.9%

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

      1. associate-*r/ 81.7%

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

      2. associate-*r/ 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. associate-*r/ 85.9%

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

   9. Simplified 85.9%

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

   if 1.94999999999999995e-122 < B

   1. Initial program 52.7%

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

      1. associate-*r/ 52.7%

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

      2. associate-*l/ 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. associate--l- 52.8%

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

      5. unpow2 52.8%

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

      6. pow2 52.8%

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

      7. hypot-def 76.3%

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

   3. Applied egg-rr 76.3%

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

   4. Taylor expanded in B around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in C around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. remove-double-neg 67.6%

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

      3. sub-neg 67.6%

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

      4. div-sub 67.6%

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

      5. *-inverses 67.6%

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

      6. neg-mul-1 67.6%

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

      7. associate-*r/ 67.6%

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

      8. cancel-sign-sub-inv 67.6%

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

      9. metadata-eval 67.6%

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

      10. *-lft-identity 67.6%

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

      11. distribute-lft-in 67.6%

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

      12. metadata-eval 67.6%

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

      13. mul-1-neg 67.6%

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

      14. unsub-neg 67.6%

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

   9. Simplified 67.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2.8 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-274}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 63.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1100000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1100000.0)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (if (<= A -1.5e-202)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
     (* (* 180.0 (atan (/ (- C (+ A B)) B))) (/ 1.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1100000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - (A + B)) / B))) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1100000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - (A + B)) / B))) * (1.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1100000.0:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	elif A <= -1.5e-202:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - (A + B)) / B))) * (1.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1100000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	elseif (A <= -1.5e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + B)) / B))) * Float64(1.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1100000.0)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	elseif (A <= -1.5e-202)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 * atan(((C - (A + B)) / B))) * (1.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1100000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.5e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.1e6

   1. Initial program 20.3%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.0%

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

   6. Simplified 78.0%

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

   if -1.1e6 < A < -1.50000000000000005e-202

   1. Initial program 64.4%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in B around -inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. div-sub 64.0%

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

   6. Simplified 64.0%

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

   if -1.50000000000000005e-202 < A

   1. Initial program 69.7%

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

      1. associate-*r/ 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-un-lft-identity 69.7%

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

      4. associate--l- 69.7%

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

      5. unpow2 69.7%

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

      6. pow2 69.7%

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

      7. hypot-def 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in B around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   6. Simplified 68.3%

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

      1. div-inv 68.3%

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

      2. associate--l- 68.3%

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

   8. Applied egg-rr 68.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1100000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\right) \cdot \frac{1}{\pi}\\ \end{array} \]

Alternative 11: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -2.4e-61)
     t_0
     (if (<= B -3.8e-96)
       (/ (* 180.0 (atan (/ C B))) PI)
       (if (<= B -5.6e-149)
         t_0
         (if (<= B 5.2e-97)
           (/ (* 180.0 (atan (- (/ A B)))) PI)
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -2.4e-61) {
		tmp = t_0;
	} else if (B <= -3.8e-96) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= -5.6e-149) {
		tmp = t_0;
	} else if (B <= 5.2e-97) {
		tmp = (180.0 * atan(-(A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -2.4e-61) {
		tmp = t_0;
	} else if (B <= -3.8e-96) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= -5.6e-149) {
		tmp = t_0;
	} else if (B <= 5.2e-97) {
		tmp = (180.0 * Math.atan(-(A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -2.4e-61:
		tmp = t_0
	elif B <= -3.8e-96:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= -5.6e-149:
		tmp = t_0
	elif B <= 5.2e-97:
		tmp = (180.0 * math.atan(-(A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -2.4e-61)
		tmp = t_0;
	elseif (B <= -3.8e-96)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= -5.6e-149)
		tmp = t_0;
	elseif (B <= 5.2e-97)
		tmp = Float64(Float64(180.0 * atan(Float64(-Float64(A / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -2.4e-61)
		tmp = t_0;
	elseif (B <= -3.8e-96)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= -5.6e-149)
		tmp = t_0;
	elseif (B <= 5.2e-97)
		tmp = (180.0 * atan(-(A / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.4e-61], t$95$0, If[LessEqual[B, -3.8e-96], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -5.6e-149], t$95$0, If[LessEqual[B, 5.2e-97], N[(N[(180.0 * N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.4000000000000001e-61 or -3.8000000000000001e-96 < B < -5.5999999999999997e-149

   1. Initial program 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in B around -inf 55.1%

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

   if -2.4000000000000001e-61 < B < -3.8000000000000001e-96

   1. Initial program 51.9%

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

      1. associate-*r/ 51.9%

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

      2. associate-*l/ 51.9%

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

      3. *-un-lft-identity 51.9%

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

      4. associate--l- 51.8%

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

      5. unpow2 51.8%

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

      6. pow2 51.8%

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

      7. hypot-def 61.8%

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

   3. Applied egg-rr 61.8%

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

   4. Taylor expanded in B around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in C around inf 51.9%

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

   if -5.5999999999999997e-149 < B < 5.20000000000000014e-97

   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. Step-by-step derivation

      1. associate-*r/ 63.3%

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

      2. associate-*l/ 63.3%

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

      3. *-un-lft-identity 63.3%

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

      4. associate--l- 60.7%

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

      5. unpow2 60.7%

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

      6. pow2 60.7%

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

      7. hypot-def 64.5%

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

   3. Applied egg-rr 64.5%

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

   4. Taylor expanded in B around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in A around inf 40.6%

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

      1. associate-*r/ 40.6%

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

      2. neg-mul-1 40.6%

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

   9. Simplified 40.6%

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

   if 5.20000000000000014e-97 < B

   1. Initial program 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in B around inf 55.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.4 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 46.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -1.55e-61)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 6.6e-210)
       t_0
       (if (<= B 6e-126)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 2.15e-122) 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 <= -1.55e-61) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.6e-210) {
		tmp = t_0;
	} else if (B <= 6e-126) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.15e-122) {
		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 <= -1.55e-61) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.6e-210) {
		tmp = t_0;
	} else if (B <= 6e-126) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.15e-122) {
		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 <= -1.55e-61:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.6e-210:
		tmp = t_0
	elif B <= 6e-126:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.15e-122:
		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 <= -1.55e-61)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.6e-210)
		tmp = t_0;
	elseif (B <= 6e-126)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.15e-122)
		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 <= -1.55e-61)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.6e-210)
		tmp = t_0;
	elseif (B <= 6e-126)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.15e-122)
		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, -1.55e-61], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.6e-210], t$95$0, If[LessEqual[B, 6e-126], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.15e-122], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.54999999999999997e-61

   1. Initial program 57.2%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in B around -inf 57.8%

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

   if -1.54999999999999997e-61 < B < 6.6e-210 or 6.0000000000000003e-126 < B < 2.15000000000000009e-122

   1. Initial program 63.7%

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

      1. associate-*r/ 63.7%

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

      2. associate-*l/ 63.7%

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

      3. *-un-lft-identity 63.7%

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

      4. associate--l- 60.9%

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

      5. unpow2 60.9%

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

      6. pow2 60.9%

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

      7. hypot-def 63.7%

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

   3. Applied egg-rr 63.7%

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

   4. Taylor expanded in B around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in C around inf 37.3%

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

   if 6.6e-210 < B < 6.0000000000000003e-126

   1. Initial program 44.4%

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

   3. Simplified 43.9%

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

   4. Taylor expanded in C around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-rgt1-in 39.4%

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

      3. metadata-eval 39.4%

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

      4. mul0-lft 39.4%

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

      5. distribute-frac-neg 39.4%

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

      6. metadata-eval 39.4%

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

   6. Simplified 39.4%

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

   if 2.15000000000000009e-122 < B

   1. Initial program 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in B around inf 53.5%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.6 \cdot 10^{-210}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 61.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;A \leq -7000000:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + t_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= A -7000000.0)
     (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
     (if (<= A -1.6e-202)
       (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
       (* 180.0 (/ (atan (+ -1.0 t_0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (A <= -7000000.0) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= -1.6e-202) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + t_0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (A <= -7000000.0) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= -1.6e-202) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + t_0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if A <= -7000000.0:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= -1.6e-202:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + t_0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (A <= -7000000.0)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= -1.6e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + t_0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (A <= -7000000.0)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= -1.6e-202)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + t_0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[A, -7000000.0], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.6e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if A < -7e6

   1. Initial program 20.3%

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

   3. Simplified 17.1%

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

   4. Taylor expanded in A around -inf 69.4%

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

      1. associate-*r/ 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in B around 0 69.4%

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

      1. associate-*r/ 69.5%

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

      2. associate-*r/ 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/l* 70.1%

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

      5. *-commutative 70.1%

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

      6. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

   if -7e6 < A < -1.6000000000000001e-202

   1. Initial program 64.4%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in B around -inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. div-sub 64.0%

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

   6. Simplified 64.0%

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

   if -1.6000000000000001e-202 < A

   1. Initial program 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in B around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate--r+ 67.5%

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

      3. div-sub 68.3%

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

   6. Simplified 68.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7000000:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 63.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;A \leq -7200000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + t_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= A -7200000.0)
     (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
     (if (<= A -1.5e-202)
       (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
       (* 180.0 (/ (atan (+ -1.0 t_0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (A <= -7200000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + t_0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (A <= -7200000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + t_0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if A <= -7200000.0:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	elif A <= -1.5e-202:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + t_0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (A <= -7200000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	elseif (A <= -1.5e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + t_0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (A <= -7200000.0)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	elseif (A <= -1.5e-202)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + t_0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[A, -7200000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.5e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.2e6

   1. Initial program 20.3%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.0%

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

   6. Simplified 78.0%

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

   if -7.2e6 < A < -1.50000000000000005e-202

   1. Initial program 64.4%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in B around -inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. div-sub 64.0%

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

   6. Simplified 64.0%

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

   if -1.50000000000000005e-202 < A

   1. Initial program 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in B around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate--r+ 67.5%

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

      3. div-sub 68.3%

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

   6. Simplified 68.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7200000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 63.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -175000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -175000.0)
   (* (/ 180.0 PI) (atan (/ (* -0.5 B) (- C A))))
   (if (<= A -1.5e-202)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
     (/ (* 180.0 (atan (/ (- (- C B) A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -175000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((((C - B) - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -175000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * B) / (C - A)));
	} else if (A <= -1.5e-202) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((((C - B) - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -175000.0:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * B) / (C - A)))
	elif A <= -1.5e-202:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan((((C - B) - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -175000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * B) / Float64(C - A))));
	elseif (A <= -1.5e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - B) - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -175000.0)
		tmp = (180.0 / pi) * atan(((-0.5 * B) / (C - A)));
	elseif (A <= -1.5e-202)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 * atan((((C - B) - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -175000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.5e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -175000

   1. Initial program 20.3%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.0%

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

   6. Simplified 78.0%

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

   if -175000 < A < -1.50000000000000005e-202

   1. Initial program 64.4%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in B around -inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. div-sub 64.0%

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

   6. Simplified 64.0%

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

   if -1.50000000000000005e-202 < A

   1. Initial program 69.7%

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

      1. associate-*r/ 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-un-lft-identity 69.7%

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

      4. associate--l- 69.7%

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

      5. unpow2 69.7%

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

      6. pow2 69.7%

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

      7. hypot-def 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in B around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   6. Simplified 68.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -175000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot B}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 53.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.05 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.05e-250)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 9.5e-142)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e-250) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 9.5e-142) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e-250) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 9.5e-142) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.05e-250:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 9.5e-142:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.05e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 9.5e-142)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.05e-250)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 9.5e-142)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.05e-250], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.5e-142], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.05000000000000008e-250

   1. Initial program 40.1%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in A around -inf 56.7%

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

      1. associate-*r/ 56.7%

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

   6. Simplified 56.7%

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

   if -2.05000000000000008e-250 < A < 9.49999999999999967e-142

   1. Initial program 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in B around inf 37.0%

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

   if 9.49999999999999967e-142 < A

   1. Initial program 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in C around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. mul-1-neg 72.2%

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

      3. +-commutative 72.2%

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

      4. unpow2 72.2%

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

      5. unpow2 72.2%

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

      6. hypot-def 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in B around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.05 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.5 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 53.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e-249)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 9.2e-142)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-249) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 9.2e-142) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-249) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 9.2e-142) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e-249:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 9.2e-142:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e-249)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 9.2e-142)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e-249)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 9.2e-142)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e-249], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.2e-142], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.09999999999999993e-249

   1. Initial program 40.1%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in A around -inf 56.7%

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

      1. associate-*r/ 56.7%

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

   6. Simplified 56.7%

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

      1. associate-*r/ 56.8%

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

      2. *-commutative 56.8%

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

   8. Applied egg-rr 56.8%

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

   9. Taylor expanded in B around 0 56.7%

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

       1. associate-*r/ 56.7%

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

       2. *-commutative 56.7%

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

       3. associate-*r/ 56.8%

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

       4. associate-*l/ 56.8%

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

       5. *-commutative 56.8%

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

       6. *-commutative 56.8%

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

       7. associate-*r/ 56.8%

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

   11. Simplified 56.8%

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

   if -2.09999999999999993e-249 < A < 9.20000000000000009e-142

   1. Initial program 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in B around inf 37.0%

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

   if 9.20000000000000009e-142 < A

   1. Initial program 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in C around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. mul-1-neg 72.2%

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

      3. +-commutative 72.2%

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

      4. unpow2 72.2%

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

      5. unpow2 72.2%

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

      6. hypot-def 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in B around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18: 53.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{-250}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.8e-250)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 2.8e-145)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e-250) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 2.8e-145) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e-250) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 2.8e-145) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.8e-250:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 2.8e-145:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.8e-250)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 2.8e-145)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.8e-250)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 2.8e-145)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.8e-250], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.8e-145], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.8000000000000004e-250

   1. Initial program 40.1%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in A around -inf 56.7%

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

      1. associate-*r/ 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in B around 0 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*r/ 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-/l* 57.0%

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

      5. *-commutative 57.0%

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

      6. associate-*r/ 57.0%

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

   9. Simplified 57.0%

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

   if -5.8000000000000004e-250 < A < 2.8000000000000001e-145

   1. Initial program 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in B around inf 37.0%

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

   if 2.8000000000000001e-145 < A

   1. Initial program 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in C around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. mul-1-neg 72.2%

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

      3. +-commutative 72.2%

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

      4. unpow2 72.2%

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

      5. unpow2 72.2%

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

      6. hypot-def 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in B around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{-250}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19: 45.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.4 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.3e-183)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.4e-126)
     (* 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 <= -2.3e-183) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.4e-126) {
		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 <= -2.3e-183) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.4e-126) {
		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 <= -2.3e-183:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.4e-126:
		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 <= -2.3e-183)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.4e-126)
		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 <= -2.3e-183)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.4e-126)
		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, -2.3e-183], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.4e-126], 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 < -2.30000000000000016e-183

   1. Initial program 56.2%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in B around -inf 47.9%

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

   if -2.30000000000000016e-183 < B < 9.40000000000000035e-126

   1. Initial program 61.2%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in C around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. distribute-rgt1-in 33.1%

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

      3. metadata-eval 33.1%

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

      4. mul0-lft 33.1%

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

      5. distribute-frac-neg 33.1%

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

      6. metadata-eval 33.1%

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

   6. Simplified 33.1%

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

   if 9.40000000000000035e-126 < B

   1. Initial program 53.6%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in B around inf 52.8%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.4 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20: 51.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.2 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.2e-97)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.2e-97) {
		tmp = 180.0 * (atan((1.0 - (A / 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 <= 5.2e-97) {
		tmp = 180.0 * (Math.atan((1.0 - (A / 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 <= 5.2e-97:
		tmp = 180.0 * (math.atan((1.0 - (A / 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 <= 5.2e-97)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / 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 <= 5.2e-97)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.2e-97], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $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 < 5.20000000000000014e-97

   1. Initial program 59.7%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in C around 0 47.0%

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

      1. associate-*r/ 47.0%

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

      2. mul-1-neg 47.0%

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

      3. +-commutative 47.0%

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

      4. unpow2 47.0%

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

      5. unpow2 47.0%

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

      6. hypot-def 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in B around -inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. unsub-neg 50.8%

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

   9. Simplified 50.8%

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

   if 5.20000000000000014e-97 < B

   1. Initial program 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in B around inf 55.0%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.2 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21: 40.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 57.7%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around -inf 40.8%

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

   if -1.999999999999994e-310 < B

   1. Initial program 55.3%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in B around inf 41.2%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 20.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 56.4%

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

3. Simplified 55.6%

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

4. Taylor expanded in B around inf 22.7%

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

5. Final simplification 22.7%

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

Reproduce

herbie shell --seed 2023283 
(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)))