ABCF->ab-angle angle

Percentage Accurate: 54.7% → 81.4%

Time: 14.7s

Alternatives: 18

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.7% 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: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.16 \cdot 10^{+148}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.16e+148)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (/ (* 180.0 (atan (/ (- (- C A) (hypot B (- A C))) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.16e+148) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.16e+148) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot(B, (A - C))) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.16e+148:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot(B, (A - C))) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.16e+148)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.16e+148)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.16e+148], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.1599999999999999e148

   1. Initial program 5.8%

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

      1. associate-*r/ 5.8%

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

   4. Applied egg-rr 54.3%

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

   5. Taylor expanded in A around -inf 83.3%

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

   if -1.1599999999999999e148 < A

   1. Initial program 65.9%

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

      1. associate-*r/ 65.9%

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

   4. Applied egg-rr 84.1%

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

Alternative 2: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.6e+59)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 3.8e-7)
     (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+59) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 3.8e-7) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+59) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 3.8e-7) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.6e+59:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 3.8e-7:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.6e+59)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 3.8e-7)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.6e+59)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 3.8e-7)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.6e+59], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.8e-7], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.59999999999999999e59

   1. Initial program 23.4%

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

      1. associate-*r/ 23.4%

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in A around -inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. distribute-lft-out 75.7%

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

      3. associate-*r* 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -2.59999999999999999e59 < A < 3.80000000000000015e-7

   1. Initial program 60.9%

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

      1. associate-*r/ 60.9%

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

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in A around 0 58.7%

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

      1. +-commutative 58.7%

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

      2. unpow2 58.7%

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

      3. unpow2 58.7%

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

      4. hypot-define 78.1%

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

   7. Simplified 78.1%

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

   if 3.80000000000000015e-7 < A

   1. Initial program 80.9%

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

   3. Taylor expanded in C around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unpow2 80.1%

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

      4. unpow2 80.1%

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

      5. hypot-define 93.4%

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

   5. Simplified 93.4%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{+58}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+33}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A - C}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e+58)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 5e+33)
     (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
     (* (atan (- -1.0 (/ (- A C) B))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+58) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 5e+33) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else {
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+58) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 5e+33) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else {
		tmp = Math.atan((-1.0 - ((A - C) / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e+58:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 5e+33:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	else:
		tmp = math.atan((-1.0 - ((A - C) / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e+58)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 5e+33)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(Float64(A - C) / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e+58)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 5e+33)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	else
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e+58], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e+33], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.0000000000000005e58

   1. Initial program 23.4%

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

      1. associate-*r/ 23.4%

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in A around -inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. distribute-lft-out 75.7%

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

      3. associate-*r* 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -6.0000000000000005e58 < A < 4.99999999999999973e33

   1. Initial program 61.0%

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

      1. associate-*r/ 61.0%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in A around 0 58.4%

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

      1. +-commutative 58.4%

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

      2. unpow2 58.4%

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

      3. unpow2 58.4%

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

      4. hypot-define 77.9%

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

   7. Simplified 77.9%

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

   if 4.99999999999999973e33 < A

   1. Initial program 83.1%

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

      1. associate-*r/ 83.1%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in B around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. associate--r+ 90.6%

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

      3. div-sub 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in C around -inf 92.5%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 92.5%

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

      4. sub-neg 92.5%

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

      5. metadata-eval 92.5%

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

      6. +-commutative 92.5%

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

      7. mul-1-neg 92.5%

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

      8. unsub-neg 92.5%

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

      9. mul-1-neg 92.5%

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

      10. sub-neg 92.5%

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

   10. Simplified 92.5%

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

Alternative 4: 75.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A - C}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.2e+59)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 4.6e+33)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* (atan (- -1.0 (/ (- A C) B))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e+59) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 4.6e+33) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e+59) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 4.6e+33) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((-1.0 - ((A - C) / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.2e+59:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 4.6e+33:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = math.atan((-1.0 - ((A - C) / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.2e+59)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 4.6e+33)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(Float64(A - C) / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e+59)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 4.6e+33)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.2e+59], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 4.6e+33], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.2000000000000001e59

   1. Initial program 23.4%

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

      1. associate-*r/ 23.4%

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in A around -inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. distribute-lft-out 75.7%

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

      3. associate-*r* 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -1.2000000000000001e59 < A < 4.60000000000000021e33

   1. Initial program 61.0%

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

   3. Taylor expanded in A around 0 58.4%

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

      1. +-commutative 58.4%

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

      2. unpow2 58.4%

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

      3. unpow2 58.4%

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

      4. hypot-define 77.9%

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

   5. Simplified 77.9%

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

   if 4.60000000000000021e33 < A

   1. Initial program 83.1%

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

      1. associate-*r/ 83.1%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in B around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. associate--r+ 90.6%

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

      3. div-sub 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in C around -inf 92.5%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 92.5%

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

      4. sub-neg 92.5%

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

      5. metadata-eval 92.5%

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

      6. +-commutative 92.5%

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

      7. mul-1-neg 92.5%

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

      8. unsub-neg 92.5%

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

      9. mul-1-neg 92.5%

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

      10. sub-neg 92.5%

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

   10. Simplified 92.5%

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

Alternative 5: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+147}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e+147)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+147) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+147) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e+147:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e+147)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e+147)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e+147], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.55e147

   1. Initial program 5.8%

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

      1. associate-*r/ 5.8%

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

   4. Applied egg-rr 54.3%

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

   5. Taylor expanded in A around -inf 83.3%

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

   if -1.55e147 < A

   1. Initial program 65.9%

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

      1. associate-*l/ 65.9%

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

      2. *-lft-identity 65.9%

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

      3. +-commutative 65.9%

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

      4. unpow2 65.9%

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

      5. unpow2 65.9%

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

      6. hypot-define 84.0%

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

   3. Simplified 84.0%

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

Alternative 6: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+59)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+59) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+59) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+59:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+59)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+59)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+59], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.7000000000000001e59

   1. Initial program 23.4%

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

      1. associate-*r/ 23.4%

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in A around -inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. distribute-lft-out 75.7%

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

      3. associate-*r* 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -2.7000000000000001e59 < A

   1. Initial program 67.2%

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

   3. Simplified 85.8%

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

Alternative 7: 65.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-185}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A - C}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.4e-140)
   (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)
   (if (<= B -4.5e-185)
     (/ (* 180.0 (atan 0.0)) PI)
     (* (atan (- -1.0 (/ (- A C) B))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-140) {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	} else if (B <= -4.5e-185) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-140) {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	} else if (B <= -4.5e-185) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = Math.atan((-1.0 - ((A - C) / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.4e-140:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	elif B <= -4.5e-185:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = math.atan((-1.0 - ((A - C) / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.4e-140)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	elseif (B <= -4.5e-185)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(Float64(A - C) / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.4e-140)
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	elseif (B <= -4.5e-185)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.4e-140], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -4.5e-185], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.40000000000000008e-140

   1. Initial program 55.7%

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

      1. associate-*r/ 55.7%

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

   4. Applied egg-rr 73.6%

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

   5. Taylor expanded in B around -inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. div-sub 70.3%

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

   7. Simplified 70.3%

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

   if -3.40000000000000008e-140 < B < -4.5000000000000001e-185

   1. Initial program 21.1%

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

      1. associate-*r/ 21.1%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in C around inf 65.1%

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

      1. distribute-rgt1-in 65.1%

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

      2. metadata-eval 65.1%

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

      3. mul0-lft 65.1%

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

      4. div0 65.1%

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

      5. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   if -4.5000000000000001e-185 < B

   1. Initial program 63.2%

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

      1. associate-*r/ 63.2%

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

   4. Applied egg-rr 84.5%

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

   5. Taylor expanded in B around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. associate--r+ 71.6%

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

      3. div-sub 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in C around -inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-/l* 72.3%

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

      4. sub-neg 72.3%

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

      5. metadata-eval 72.3%

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

      6. +-commutative 72.3%

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

      7. mul-1-neg 72.3%

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

      8. unsub-neg 72.3%

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

      9. mul-1-neg 72.3%

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

      10. sub-neg 72.3%

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

   10. Simplified 72.3%

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

Alternative 8: 65.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-185}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A - C}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.4e-140)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B -4.4e-185)
     (/ (* 180.0 (atan 0.0)) PI)
     (* (atan (- -1.0 (/ (- A C) B))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-140) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= -4.4e-185) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-140) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= -4.4e-185) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = Math.atan((-1.0 - ((A - C) / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.4e-140:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= -4.4e-185:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = math.atan((-1.0 - ((A - C) / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.4e-140)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= -4.4e-185)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(Float64(A - C) / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.4e-140)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= -4.4e-185)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = atan((-1.0 - ((A - C) / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.4e-140], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.4e-185], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.40000000000000008e-140

   1. Initial program 55.7%

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

   3. Taylor expanded in B around -inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. div-sub 70.2%

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

   5. Simplified 70.2%

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

   if -3.40000000000000008e-140 < B < -4.4000000000000001e-185

   1. Initial program 21.1%

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

      1. associate-*r/ 21.1%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in C around inf 65.1%

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

      1. distribute-rgt1-in 65.1%

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

      2. metadata-eval 65.1%

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

      3. mul0-lft 65.1%

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

      4. div0 65.1%

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

      5. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   if -4.4000000000000001e-185 < B

   1. Initial program 63.2%

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

      1. associate-*r/ 63.2%

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

   4. Applied egg-rr 84.5%

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

   5. Taylor expanded in B around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. associate--r+ 71.6%

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

      3. div-sub 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in C around -inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-/l* 72.3%

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

      4. sub-neg 72.3%

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

      5. metadata-eval 72.3%

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

      6. +-commutative 72.3%

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

      7. mul-1-neg 72.3%

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

      8. unsub-neg 72.3%

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

      9. mul-1-neg 72.3%

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

      10. sub-neg 72.3%

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

   10. Simplified 72.3%

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

Alternative 9: 59.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1450:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.8e+50)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 1450.0)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+50) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 1450.0) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+50) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= 1450.0) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.8e+50:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= 1450.0:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.8e+50)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 1450.0)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.8e+50)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= 1450.0)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.8e+50], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1450.0], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.8000000000000004e50

   1. Initial program 84.9%

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

   3. Taylor expanded in B around -inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. div-sub 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in A around 0 83.3%

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

   if -4.8000000000000004e50 < C < 1450

   1. Initial program 59.3%

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

      1. associate-*r/ 59.3%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in B around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. associate--r+ 59.7%

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

      3. div-sub 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in C around 0 57.5%

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

      1. distribute-lft-in 57.5%

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

      2. metadata-eval 57.5%

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

      3. mul-1-neg 57.5%

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

      4. unsub-neg 57.5%

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

   10. Simplified 57.5%

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

   if 1450 < C

   1. Initial program 27.1%

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

   3. Taylor expanded in C around inf 66.5%

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

   4. Taylor expanded in A around inf 66.5%

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

   6. Simplified 66.7%

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

Alternative 10: 56.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.3e+57)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 1.4e+31)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.3e+57) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.4e+31) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.3e+57) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.4e+31) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.3e+57:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.4e+31:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.3e+57)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.4e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.3e+57)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.4e+31)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.3e+57], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.30000000000000033e57

   1. Initial program 23.0%

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

   3. Taylor expanded in A around -inf 70.7%

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

      1. associate-*r/ 70.7%

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

   5. Simplified 70.7%

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

   if -4.30000000000000033e57 < A < 1.40000000000000008e31

   1. Initial program 61.4%

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

   3. Taylor expanded in B around -inf 48.7%

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

      1. associate--l+ 48.7%

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

      2. div-sub 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in A around 0 46.3%

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

   if 1.40000000000000008e31 < A

   1. Initial program 83.1%

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

      1. associate-*l/ 83.1%

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

      2. *-lft-identity 83.1%

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

      3. +-commutative 83.1%

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

      4. unpow2 83.1%

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

      5. unpow2 83.1%

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

      6. hypot-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in A around inf 77.6%

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

      1. *-commutative 77.6%

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

   7. Simplified 77.6%

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

Alternative 11: 56.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.2e+56)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 2.7e+33)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ A (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+56) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 2.7e+33) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+56) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 2.7e+33) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.2e+56:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 2.7e+33:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.2e+56)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 2.7e+33)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.2e+56)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 2.7e+33)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((A / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.2e+56], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.7e+33], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.20000000000000009e56

   1. Initial program 23.0%

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

   3. Taylor expanded in A around -inf 70.7%

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

      1. associate-*r/ 70.7%

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

   5. Simplified 70.7%

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

   if -6.20000000000000009e56 < A < 2.69999999999999991e33

   1. Initial program 61.4%

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

   3. Taylor expanded in B around -inf 48.7%

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

      1. associate--l+ 48.7%

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

      2. div-sub 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in A around 0 46.3%

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

   if 2.69999999999999991e33 < A

   1. Initial program 83.1%

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

   3. Taylor expanded in B around -inf 80.2%

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

      1. associate--l+ 80.2%

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

      2. div-sub 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in A around inf 76.9%

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

      1. associate-*r/ 76.9%

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

      2. mul-1-neg 76.9%

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

   8. Simplified 76.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.42 \cdot 10^{-241}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4400:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.42e-241)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 4400.0)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.42e-241) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 4400.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.42e-241) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= 4400.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.42e-241:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= 4400.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.42e-241)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 4400.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.42e-241)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= 4400.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.42e-241], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4400.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.41999999999999992e-241

   1. Initial program 73.7%

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

   3. Taylor expanded in B around -inf 69.3%

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

      1. associate--l+ 69.3%

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

      2. div-sub 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in A around 0 63.4%

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

   if -1.41999999999999992e-241 < C < 4400

   1. Initial program 58.0%

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

   3. Taylor expanded in B around inf 40.8%

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

   if 4400 < C

   1. Initial program 27.1%

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

   3. Taylor expanded in C around inf 66.5%

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

   4. Taylor expanded in B around inf 49.3%

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

      1. distribute-rgt1-in 49.3%

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

      2. metadata-eval 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{{B}^{2}} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      3. mul0-lft 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \frac{\color{blue}{0}}{{B}^{2}} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      4. div0 66.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \color{blue}{0} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      5. metadata-eval 66.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(\color{blue}{0} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      6. neg-sub0 66.4%

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

      7. associate-*r/ 66.4%

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

      8. metadata-eval 66.4%

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

      9. distribute-neg-frac 66.4%

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

      10. metadata-eval 66.4%

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

   6. Simplified 66.4%

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

Alternative 13: 47.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 370:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.2e-182)
   (/ (* 180.0 (atan (/ C B))) PI)
   (if (<= C 370.0)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-182) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (C <= 370.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-182) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (C <= 370.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.2e-182:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif C <= 370.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.2e-182)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (C <= 370.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.2e-182)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (C <= 370.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.2e-182], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 370.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.2000000000000001e-182

   1. Initial program 75.2%

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

      1. associate-*r/ 75.2%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in B around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. associate--r+ 74.3%

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

      3. div-sub 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in C around inf 57.1%

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

   if -4.2000000000000001e-182 < C < 370

   1. Initial program 58.0%

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

   3. Taylor expanded in B around inf 38.3%

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

   if 370 < C

   1. Initial program 27.1%

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

   3. Taylor expanded in C around inf 66.5%

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

   4. Taylor expanded in B around inf 49.3%

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

      1. distribute-rgt1-in 49.3%

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

      2. metadata-eval 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{{B}^{2}} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      3. mul0-lft 49.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \frac{\color{blue}{0}}{{B}^{2}} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      4. div0 66.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-1 \cdot \color{blue}{0} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      5. metadata-eval 66.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \left(\color{blue}{0} - 0.5 \cdot \frac{1}{C}\right)\right)}{\pi} \]

      6. neg-sub0 66.4%

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

      7. associate-*r/ 66.4%

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

      8. metadata-eval 66.4%

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

      9. distribute-neg-frac 66.4%

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

      10. metadata-eval 66.4%

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

   6. Simplified 66.4%

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

Alternative 14: 45.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-27}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.6e+78)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9e-27)
     (/ (* 180.0 (atan (/ C B))) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.6e+78) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9e-27) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.6e+78) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9e-27) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.6e+78:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9e-27:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.6e+78)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9e-27)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.6e+78)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9e-27)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.6e+78], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-27], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.59999999999999997e78

   1. Initial program 51.3%

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

   3. Taylor expanded in B around -inf 64.4%

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

   if -1.59999999999999997e78 < B < 9.0000000000000003e-27

   1. Initial program 61.9%

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

      1. associate-*r/ 61.9%

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

   4. Applied egg-rr 76.7%

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

   5. Taylor expanded in B around inf 55.7%

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

      1. +-commutative 55.7%

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

      2. associate--r+ 55.7%

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

      3. div-sub 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in C around inf 38.9%

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

   if 9.0000000000000003e-27 < B

   1. Initial program 57.5%

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

   3. Taylor expanded in B around inf 63.3%

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

Alternative 15: 61.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.6e-212)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (/ (* 180.0 (atan (+ -1.0 (/ C B)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.6e-212) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 + (C / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.6e-212) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 + (C / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 2.6e-212:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 + (C / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 2.6e-212)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(C / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 2.6e-212)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 * atan((-1.0 + (C / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 2.6e-212], 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[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 2.6e-212

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf 62.7%

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

      1. associate--l+ 62.7%

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

      2. div-sub 63.4%

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

   5. Simplified 63.4%

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

   if 2.6e-212 < B

   1. Initial program 61.7%

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

      1. associate-*r/ 61.7%

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in B around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. associate--r+ 75.9%

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

      3. div-sub 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in A around 0 69.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-157}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-136)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.75e-157)
     (/ (* 180.0 (atan 0.0)) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-136) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.75e-157) {
		tmp = (180.0 * atan(0.0)) / ((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 <= -1.9e-136) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.75e-157) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.9e-136:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.75e-157:
		tmp = (180.0 * math.atan(0.0)) / 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 <= -1.9e-136)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.75e-157)
		tmp = Float64(Float64(180.0 * atan(0.0)) / 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 <= -1.9e-136)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.75e-157)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e-136], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.75e-157], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.9000000000000001e-136

   1. Initial program 55.7%

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

   3. Taylor expanded in B around -inf 41.0%

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

   if -1.9000000000000001e-136 < B < 1.7500000000000001e-157

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in C around inf 33.9%

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

      1. distribute-rgt1-in 33.9%

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

      2. metadata-eval 33.9%

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

      3. mul0-lft 33.9%

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

      4. div0 33.9%

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

      5. metadata-eval 33.9%

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

   7. Simplified 33.9%

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

   if 1.7500000000000001e-157 < B

   1. Initial program 62.4%

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

   3. Taylor expanded in B around inf 55.6%

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

Alternative 17: 39.7% accurate, 3.8× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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, -5e-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 < -4.999999999999985e-310

   1. Initial program 54.7%

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

   3. Taylor expanded in B around -inf 33.0%

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

   if -4.999999999999985e-310 < B

   1. Initial program 62.5%

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

   3. Taylor expanded in B around inf 46.3%

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

Alternative 18: 21.3% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.6%

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

3. Taylor expanded in B around inf 24.1%

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

Reproduce

herbie shell --seed 2024185 
(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)))