ABCF->ab-angle angle

Percentage Accurate: 53.3% → 80.8%

Time: 18.0s

Alternatives: 19

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \left(-0.5 \cdot \frac{A}{{C}^{2}} - \frac{0.5}{C}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 8.2e+49)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (* 180.0 (/ (atan (* B (- (* -0.5 (/ A (pow C 2.0))) (/ 0.5 C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.2e+49) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * ((-0.5 * (A / pow(C, 2.0))) - (0.5 / C)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.2e+49) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * ((-0.5 * (A / Math.pow(C, 2.0))) - (0.5 / C)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 8.2e+49:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * ((-0.5 * (A / math.pow(C, 2.0))) - (0.5 / C)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 8.2e+49)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(Float64(-0.5 * Float64(A / (C ^ 2.0))) - Float64(0.5 / C)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 8.2e+49)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = 180.0 * (atan((B * ((-0.5 * (A / (C ^ 2.0))) - (0.5 / C)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 8.2e+49], 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], N[(180.0 * N[(N[ArcTan[N[(B * N[(N[(-0.5 * N[(A / N[Power[C, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.5 / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 8.2e49

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

      3. +-commutative 59.8%

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

      4. unpow2 59.8%

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

      5. unpow2 59.8%

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

      6. hypot-define 86.1%

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

   3. Simplified 86.1%

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

   if 8.2e49 < C

   1. Initial program 16.5%

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

   3. Taylor expanded in C around inf 81.5%

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

   4. Taylor expanded in B around inf 81.8%

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

      1. associate-*r/ 81.8%

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

      2. metadata-eval 81.8%

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

   6. Simplified 81.8%

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

Alternative 2: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + A \cdot \frac{B}{C}\right)}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -8.8e+42)
   (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
   (if (<= C 7.5e+49)
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI))
     (* 180.0 (/ (atan (/ (* -0.5 (+ B (* A (/ B C)))) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -8.8e+42) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else if (C <= 7.5e+49) {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -8.8e+42) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else if (C <= 7.5e+49) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -8.8e+42:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	elif C <= 7.5e+49:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -8.8e+42)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	elseif (C <= 7.5e+49)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(A * Float64(B / C)))) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -8.8e+42)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	elseif (C <= 7.5e+49)
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	else
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -8.8e+42], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 7.5e+49], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(A * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.8000000000000005e42

   1. Initial program 68.4%

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

      1. associate-*r/ 68.4%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in A around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. unpow2 68.4%

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

      3. unpow2 68.4%

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

      4. hypot-define 95.3%

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

   7. Simplified 95.3%

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

   if -8.8000000000000005e42 < C < 7.4999999999999995e49

   1. Initial program 56.6%

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

   3. Taylor expanded in C around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unpow2 53.6%

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

      4. unpow2 53.6%

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

      5. hypot-define 79.4%

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

   5. Simplified 79.4%

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

   if 7.4999999999999995e49 < C

   1. Initial program 16.5%

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

   3. Taylor expanded in C around inf 81.5%

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

   4. Taylor expanded in C around -inf 79.6%

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

      1. distribute-rgt1-in 79.6%

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

      2. metadata-eval 79.6%

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

      3. neg-mul-1 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. mul0-lft 79.6%

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

      7. div0 79.6%

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

      8. metadata-eval 79.6%

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

      9. neg-sub0 79.6%

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

      10. mul-1-neg 79.6%

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

      11. associate-*r/ 79.6%

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

      12. distribute-lft-out 79.6%

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

      13. associate-*r* 79.6%

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

      14. metadata-eval 79.6%

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

      15. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + A \cdot \frac{B}{C}\right)}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + A \cdot \frac{B}{C}\right)}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.1e+43)
   (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
   (if (<= C 3.9e+49)
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI)
     (* 180.0 (/ (atan (/ (* -0.5 (+ B (* A (/ B C)))) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.1e+43) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else if (C <= 3.9e+49) {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.1e+43) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else if (C <= 3.9e+49) {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.1e+43:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	elif C <= 3.9e+49:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.1e+43)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	elseif (C <= 3.9e+49)
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(A * Float64(B / C)))) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.1e+43)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	elseif (C <= 3.9e+49)
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.1e+43], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 3.9e+49], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(A * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.1e43

   1. Initial program 68.4%

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

      1. associate-*r/ 68.4%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in A around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. unpow2 68.4%

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

      3. unpow2 68.4%

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

      4. hypot-define 95.3%

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

   7. Simplified 95.3%

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

   if -1.1e43 < C < 3.9000000000000001e49

   1. Initial program 56.6%

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

      1. associate-*r/ 56.5%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in C around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-neg-frac2 53.6%

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

      3. unpow2 53.6%

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

      4. unpow2 53.6%

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

      5. hypot-define 79.4%

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

   7. Simplified 79.4%

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

      1. associate-/l* 79.4%

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

      2. distribute-frac-neg2 79.4%

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

      3. atan-neg 79.4%

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

   9. Applied egg-rr 79.4%

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

       1. associate-*r/ 79.4%

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

       2. distribute-rgt-neg-out 79.4%

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

       3. distribute-lft-neg-in 79.4%

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

       4. metadata-eval 79.4%

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

   11. Simplified 79.4%

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

   if 3.9000000000000001e49 < C

   1. Initial program 16.5%

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

   3. Taylor expanded in C around inf 81.5%

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

   4. Taylor expanded in C around -inf 79.6%

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

      1. distribute-rgt1-in 79.6%

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

      2. metadata-eval 79.6%

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

      3. neg-mul-1 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. mul0-lft 79.6%

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

      7. div0 79.6%

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

      8. metadata-eval 79.6%

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

      9. neg-sub0 79.6%

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

      10. mul-1-neg 79.6%

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

      11. associate-*r/ 79.6%

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

      12. distribute-lft-out 79.6%

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

      13. associate-*r* 79.6%

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

      14. metadata-eval 79.6%

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

      15. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

Alternative 4: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + A \cdot \frac{B}{C}\right)}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -8.8e+42)
   (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
   (if (<= C 8.2e+49)
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI)
     (* 180.0 (/ (atan (/ (* -0.5 (+ B (* A (/ B C)))) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -8.8e+42) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else if (C <= 8.2e+49) {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -8.8e+42) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else if (C <= 8.2e+49) {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -8.8e+42:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	elif C <= 8.2e+49:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -8.8e+42)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	elseif (C <= 8.2e+49)
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(A * Float64(B / C)))) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -8.8e+42)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	elseif (C <= 8.2e+49)
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -8.8e+42], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.2e+49], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(A * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.8000000000000005e42

   1. Initial program 68.4%

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

   3. Taylor expanded in A around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. unpow2 68.4%

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

      3. unpow2 68.4%

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

      4. hypot-define 95.3%

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

   5. Simplified 95.3%

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

   if -8.8000000000000005e42 < C < 8.2e49

   1. Initial program 56.6%

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

      1. associate-*r/ 56.5%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in C around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-neg-frac2 53.6%

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

      3. unpow2 53.6%

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

      4. unpow2 53.6%

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

      5. hypot-define 79.4%

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

   7. Simplified 79.4%

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

      1. associate-/l* 79.4%

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

      2. distribute-frac-neg2 79.4%

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

      3. atan-neg 79.4%

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

   9. Applied egg-rr 79.4%

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

       1. associate-*r/ 79.4%

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

       2. distribute-rgt-neg-out 79.4%

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

       3. distribute-lft-neg-in 79.4%

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

       4. metadata-eval 79.4%

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

   11. Simplified 79.4%

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

   if 8.2e49 < C

   1. Initial program 16.5%

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

   3. Taylor expanded in C around inf 81.5%

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

   4. Taylor expanded in C around -inf 79.6%

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

      1. distribute-rgt1-in 79.6%

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

      2. metadata-eval 79.6%

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

      3. neg-mul-1 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. mul0-lft 79.6%

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

      7. div0 79.6%

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

      8. metadata-eval 79.6%

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

      9. neg-sub0 79.6%

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

      10. mul-1-neg 79.6%

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

      11. associate-*r/ 79.6%

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

      12. distribute-lft-out 79.6%

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

      13. associate-*r* 79.6%

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

      14. metadata-eval 79.6%

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

      15. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

Alternative 5: 73.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{+179}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.06 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.4e+179)
   (* (atan (* B (/ 0.5 A))) (/ 180.0 PI))
   (if (<= A 1.06e-41)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+179) {
		tmp = atan((B * (0.5 / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 1.06e-41) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+179) {
		tmp = Math.atan((B * (0.5 / A))) * (180.0 / Math.PI);
	} else if (A <= 1.06e-41) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.4e+179:
		tmp = math.atan((B * (0.5 / A))) * (180.0 / math.pi)
	elif A <= 1.06e-41:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.4e+179)
		tmp = Float64(atan(Float64(B * Float64(0.5 / A))) * Float64(180.0 / pi));
	elseif (A <= 1.06e-41)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.4e+179)
		tmp = atan((B * (0.5 / A))) * (180.0 / pi);
	elseif (A <= 1.06e-41)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.4e+179], N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.06e-41], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.4000000000000003e179

   1. Initial program 8.0%

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

      1. associate-*r/ 8.0%

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

   4. Applied egg-rr 59.2%

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

   5. Taylor expanded in A around -inf 91.0%

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

   6. Taylor expanded in B around 0 91.0%

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

      1. associate-*r/ 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-/l* 91.2%

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

      4. associate-*r/ 91.2%

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

      5. *-commutative 91.2%

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

      6. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

   if -6.4000000000000003e179 < A < 1.06e-41

   1. Initial program 51.6%

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

   3. Taylor expanded in A around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. unpow2 49.6%

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

      3. unpow2 49.6%

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

      4. hypot-define 75.9%

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

   5. Simplified 75.9%

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

   if 1.06e-41 < A

   1. Initial program 72.8%

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

   3. Taylor expanded in B around inf 74.8%

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

   4. Taylor expanded in C around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-in 77.9%

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

      3. metadata-eval 77.9%

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

      4. unsub-neg 77.9%

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

   6. Simplified 77.9%

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

Alternative 6: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + A \cdot \frac{B}{C}\right)}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 8.2e+49)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (* 180.0 (/ (atan (/ (* -0.5 (+ B (* A (/ B C)))) C)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.2e+49) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.2e+49) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 8.2e+49:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-0.5 * (B + (A * (B / C)))) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 8.2e+49)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(A * Float64(B / C)))) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 8.2e+49)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = 180.0 * (atan(((-0.5 * (B + (A * (B / C)))) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 8.2e+49], 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], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(A * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 8.2e49

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

      3. +-commutative 59.8%

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

      4. unpow2 59.8%

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

      5. unpow2 59.8%

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

      6. hypot-define 86.1%

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

   3. Simplified 86.1%

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

   if 8.2e49 < C

   1. Initial program 16.5%

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

   3. Taylor expanded in C around inf 81.5%

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

   4. Taylor expanded in C around -inf 79.6%

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

      1. distribute-rgt1-in 79.6%

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

      2. metadata-eval 79.6%

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

      3. neg-mul-1 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. mul0-lft 79.6%

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

      7. div0 79.6%

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

      8. metadata-eval 79.6%

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

      9. neg-sub0 79.6%

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

      10. mul-1-neg 79.6%

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

      11. associate-*r/ 79.6%

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

      12. distribute-lft-out 79.6%

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

      13. associate-*r* 79.6%

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

      14. metadata-eval 79.6%

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

      15. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

Alternative 7: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{+113}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.3e+113)
   (* (atan (* B (/ 0.5 A))) (/ 180.0 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 <= -2.3e+113) {
		tmp = atan((B * (0.5 / A))) * (180.0 / ((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 <= -2.3e+113) {
		tmp = Math.atan((B * (0.5 / A))) * (180.0 / 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 <= -2.3e+113:
		tmp = math.atan((B * (0.5 / A))) * (180.0 / 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 <= -2.3e+113)
		tmp = Float64(atan(Float64(B * Float64(0.5 / A))) * Float64(180.0 / 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 <= -2.3e+113)
		tmp = atan((B * (0.5 / A))) * (180.0 / 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, -2.3e+113], N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.29999999999999997e113

   1. Initial program 16.3%

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

      1. associate-*r/ 16.3%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in A around -inf 80.5%

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

   6. Taylor expanded in B around 0 80.6%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-/l* 80.8%

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

      4. associate-*r/ 80.8%

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

      5. *-commutative 80.8%

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

      6. associate-/l* 80.7%

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

   8. Simplified 80.7%

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

   if -2.29999999999999997e113 < A

   1. Initial program 59.4%

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

   3. Simplified 83.1%

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

Alternative 8: 46.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.3 \cdot 10^{-112}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-220}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-125}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -2.3e-112)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -9.5e-220)
       t_0
       (if (<= B 6.8e-255)
         (* 180.0 (/ (atan (- (/ A B))) PI))
         (if (<= B 2e-125)
           (/ (* 180.0 (atan 0.0)) PI)
           (if (<= B 2.5e-13) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.3e-112) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.5e-220) {
		tmp = t_0;
	} else if (B <= 6.8e-255) {
		tmp = 180.0 * (atan(-(A / B)) / ((double) M_PI));
	} else if (B <= 2e-125) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 2.5e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -2.3e-112) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.5e-220) {
		tmp = t_0;
	} else if (B <= 6.8e-255) {
		tmp = 180.0 * (Math.atan(-(A / B)) / Math.PI);
	} else if (B <= 2e-125) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 2.5e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -2.3e-112:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.5e-220:
		tmp = t_0
	elif B <= 6.8e-255:
		tmp = 180.0 * (math.atan(-(A / B)) / math.pi)
	elif B <= 2e-125:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 2.5e-13:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -2.3e-112)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.5e-220)
		tmp = t_0;
	elseif (B <= 6.8e-255)
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(A / B))) / pi));
	elseif (B <= 2e-125)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 2.5e-13)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -2.3e-112)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.5e-220)
		tmp = t_0;
	elseif (B <= 6.8e-255)
		tmp = 180.0 * (atan(-(A / B)) / pi);
	elseif (B <= 2e-125)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 2.5e-13)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.3e-112], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-220], t$95$0, If[LessEqual[B, 6.8e-255], N[(180.0 * N[(N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e-125], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.5e-13], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.29999999999999991e-112

   1. Initial program 48.3%

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

   3. Taylor expanded in B around -inf 57.2%

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

   if -2.29999999999999991e-112 < B < -9.50000000000000062e-220 or 2.00000000000000002e-125 < B < 2.49999999999999995e-13

   1. Initial program 62.8%

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

   3. Taylor expanded in B around inf 59.4%

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

   4. Taylor expanded in C around inf 45.6%

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

   if -9.50000000000000062e-220 < B < 6.79999999999999967e-255

   1. Initial program 69.0%

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

   3. Taylor expanded in B around inf 58.8%

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

   4. Taylor expanded in A around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. mul-1-neg 55.7%

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

   6. Simplified 55.7%

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

   if 6.79999999999999967e-255 < B < 2.00000000000000002e-125

   1. Initial program 33.4%

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

      1. associate-*r/ 33.4%

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

   4. Applied egg-rr 74.5%

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

   5. Taylor expanded in C around inf 55.9%

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

      1. distribute-rgt1-in 55.9%

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

      2. metadata-eval 55.9%

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

      3. mul0-lft 55.9%

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

      4. div0 55.9%

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

      5. metadata-eval 55.9%

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

   7. Simplified 55.9%

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

   if 2.49999999999999995e-13 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf 64.1%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-112}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-220}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-125}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -8.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.4 \cdot 10^{-305}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))
   (if (<= C -8.2e-57)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (if (<= C 5.4e-305)
       t_0
       (if (<= C 4.6e-90)
         (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)
         (if (<= C 2.75e-14) t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -8.2e-57) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 5.4e-305) {
		tmp = t_0;
	} else if (C <= 4.6e-90) {
		tmp = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 2.75e-14) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -8.2e-57) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else if (C <= 5.4e-305) {
		tmp = t_0;
	} else if (C <= 4.6e-90) {
		tmp = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	} else if (C <= 2.75e-14) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -8.2e-57:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	elif C <= 5.4e-305:
		tmp = t_0
	elif C <= 4.6e-90:
		tmp = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	elif C <= 2.75e-14:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -8.2e-57)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	elseif (C <= 5.4e-305)
		tmp = t_0;
	elseif (C <= 4.6e-90)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	elseif (C <= 2.75e-14)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -8.2e-57)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	elseif (C <= 5.4e-305)
		tmp = t_0;
	elseif (C <= 4.6e-90)
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	elseif (C <= 2.75e-14)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -8.2e-57], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.4e-305], t$95$0, If[LessEqual[C, 4.6e-90], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.75e-14], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -8.2000000000000003e-57

   1. Initial program 68.8%

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

   3. Taylor expanded in B around inf 79.1%

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

   4. Taylor expanded in A around 0 78.1%

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

   if -8.2000000000000003e-57 < C < 5.3999999999999998e-305 or 4.5999999999999996e-90 < C < 2.74999999999999996e-14

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf 58.8%

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

   4. Taylor expanded in C around 0 57.5%

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

      1. neg-mul-1 57.5%

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

      2. distribute-neg-in 57.5%

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

      3. metadata-eval 57.5%

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

      4. unsub-neg 57.5%

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

   6. Simplified 57.5%

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

   if 5.3999999999999998e-305 < C < 4.5999999999999996e-90

   1. Initial program 58.7%

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

      1. associate-*r/ 58.6%

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

   4. Applied egg-rr 83.6%

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

   5. Taylor expanded in C around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-neg-frac2 58.8%

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

      3. unpow2 58.8%

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

      4. unpow2 58.8%

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

      5. hypot-define 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in B around -inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   10. Simplified 66.8%

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

   if 2.74999999999999996e-14 < C

   1. Initial program 20.0%

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

      1. associate-*r/ 20.0%

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

   4. Applied egg-rr 52.6%

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

   5. Taylor expanded in C around inf 59.3%

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

      1. distribute-rgt1-in 59.3%

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

      2. metadata-eval 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in B around 0 69.0%

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

      1. associate-*r/ 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-/l* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-*l/ 69.2%

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

   10. Simplified 69.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -8.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.4 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.8 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -3.8e-110)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4e-200)
       t_0
       (if (<= B 3.6e-125)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 5.6e-13) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -3.8e-110) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4e-200) {
		tmp = t_0;
	} else if (B <= 3.6e-125) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 5.6e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -3.8e-110) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4e-200) {
		tmp = t_0;
	} else if (B <= 3.6e-125) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 5.6e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -3.8e-110:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4e-200:
		tmp = t_0
	elif B <= 3.6e-125:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 5.6e-13:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -3.8e-110)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4e-200)
		tmp = t_0;
	elseif (B <= 3.6e-125)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 5.6e-13)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -3.8e-110)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4e-200)
		tmp = t_0;
	elseif (B <= 3.6e-125)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 5.6e-13)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.8e-110], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4e-200], t$95$0, If[LessEqual[B, 3.6e-125], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.6e-13], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.7999999999999998e-110

   1. Initial program 48.3%

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

   3. Taylor expanded in B around -inf 57.2%

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

   if -3.7999999999999998e-110 < B < -3.9999999999999999e-200 or 3.6000000000000002e-125 < B < 5.6000000000000004e-13

   1. Initial program 66.8%

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

   3. Taylor expanded in B around inf 63.4%

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

   4. Taylor expanded in C around inf 48.5%

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

   if -3.9999999999999999e-200 < B < 3.6000000000000002e-125

   1. Initial program 50.4%

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

      1. associate-*r/ 50.3%

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

   4. Applied egg-rr 82.9%

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

   5. Taylor expanded in C around inf 42.5%

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

      1. distribute-rgt1-in 42.5%

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

      2. metadata-eval 42.5%

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

      3. mul0-lft 42.5%

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

      4. div0 42.5%

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

      5. metadata-eval 42.5%

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

   7. Simplified 42.5%

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

   if 5.6000000000000004e-13 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf 64.1%

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

Alternative 11: 60.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B 3.1e-254)
     t_0
     (if (<= B 3.7e-125)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= B 2.3e-13) t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= 3.1e-254) {
		tmp = t_0;
	} else if (B <= 3.7e-125) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (B <= 2.3e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= 3.1e-254) {
		tmp = t_0;
	} else if (B <= 3.7e-125) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (B <= 2.3e-13) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= 3.1e-254:
		tmp = t_0
	elif B <= 3.7e-125:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif B <= 2.3e-13:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= 3.1e-254)
		tmp = t_0;
	elseif (B <= 3.7e-125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (B <= 2.3e-13)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= 3.1e-254)
		tmp = t_0;
	elseif (B <= 3.7e-125)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (B <= 2.3e-13)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 3.1e-254], t$95$0, If[LessEqual[B, 3.7e-125], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.3e-13], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < 3.09999999999999988e-254 or 3.6999999999999999e-125 < B < 2.29999999999999979e-13

   1. Initial program 56.7%

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

   3. Taylor expanded in B around -inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. div-sub 66.9%

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

   5. Simplified 66.9%

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

   if 3.09999999999999988e-254 < B < 3.6999999999999999e-125

   1. Initial program 33.4%

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

   3. Taylor expanded in A around -inf 56.2%

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

      1. associate-*r/ 56.2%

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

   5. Simplified 56.2%

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

   if 2.29999999999999979e-13 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf 82.6%

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

   4. Taylor expanded in C around 0 74.9%

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

      1. neg-mul-1 74.9%

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

      2. distribute-neg-in 74.9%

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

      3. metadata-eval 74.9%

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

      4. unsub-neg 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3e-252)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 3.6e-125)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3e-252) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 3.6e-125) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - B) - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3e-252) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 3.6e-125) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - B) - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3e-252:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 3.6e-125:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - B) - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 3.6e-125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3e-252)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 3.6e-125)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((((C - B) - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3e-252], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-125], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 2.99999999999999995e-252

   1. Initial program 53.2%

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

   3. Taylor expanded in B around -inf 64.4%

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

      1. associate--l+ 64.4%

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

      2. div-sub 66.7%

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

   5. Simplified 66.7%

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

   if 2.99999999999999995e-252 < B < 3.6000000000000002e-125

   1. Initial program 33.4%

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

   3. Taylor expanded in A around -inf 56.2%

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

      1. associate-*r/ 56.2%

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

   5. Simplified 56.2%

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

   if 3.6000000000000002e-125 < B

   1. Initial program 56.3%

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

   3. Taylor expanded in B around inf 81.4%

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

   4. Taylor expanded in B around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{-38}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1e-38)
   (* (atan (* B (/ 0.5 A))) (/ 180.0 PI))
   (if (<= A 1.7e-135)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e-38) {
		tmp = atan((B * (0.5 / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 1.7e-135) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e-38) {
		tmp = Math.atan((B * (0.5 / A))) * (180.0 / Math.PI);
	} else if (A <= 1.7e-135) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1e-38:
		tmp = math.atan((B * (0.5 / A))) * (180.0 / math.pi)
	elif A <= 1.7e-135:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1e-38)
		tmp = Float64(atan(Float64(B * Float64(0.5 / A))) * Float64(180.0 / pi));
	elseif (A <= 1.7e-135)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1e-38)
		tmp = atan((B * (0.5 / A))) * (180.0 / pi);
	elseif (A <= 1.7e-135)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1e-38], N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.7e-135], 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[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.9999999999999996e-39

   1. Initial program 24.7%

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

      1. associate-*r/ 24.7%

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

   4. Applied egg-rr 63.9%

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

   5. Taylor expanded in A around -inf 62.4%

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

   6. Taylor expanded in B around 0 62.5%

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

      1. associate-*r/ 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-/l* 62.6%

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

      4. associate-*r/ 62.6%

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

      5. *-commutative 62.6%

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

      6. associate-/l* 62.5%

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

   8. Simplified 62.5%

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

   if -9.9999999999999996e-39 < A < 1.69999999999999995e-135

   1. Initial program 58.2%

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

   3. Taylor expanded in B around inf 55.5%

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

   4. Taylor expanded in A around 0 54.1%

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

   if 1.69999999999999995e-135 < A

   1. Initial program 69.9%

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

   3. Taylor expanded in B around inf 70.7%

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

   4. Taylor expanded in C around 0 73.1%

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

      1. neg-mul-1 73.1%

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

      2. distribute-neg-in 73.1%

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

      3. metadata-eval 73.1%

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

      4. unsub-neg 73.1%

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

   6. Simplified 73.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{-38}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.6 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.4e-42)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 7.6e-134)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e-42) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 7.6e-134) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e-42) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 7.6e-134) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.4e-42:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 7.6e-134:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.4e-42)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 7.6e-134)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.4e-42)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 7.6e-134)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.4e-42], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.6e-134], 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[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.39999999999999998e-42

   1. Initial program 24.7%

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

   3. Taylor expanded in A around -inf 62.5%

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

      1. associate-*r/ 62.5%

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

   5. Simplified 62.5%

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

   if -5.39999999999999998e-42 < A < 7.60000000000000006e-134

   1. Initial program 58.2%

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

   3. Taylor expanded in B around inf 55.5%

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

   4. Taylor expanded in A around 0 54.1%

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

   if 7.60000000000000006e-134 < A

   1. Initial program 69.9%

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

   3. Taylor expanded in B around inf 70.7%

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

   4. Taylor expanded in C around 0 73.1%

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

      1. neg-mul-1 73.1%

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

      2. distribute-neg-in 73.1%

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

      3. metadata-eval 73.1%

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

      4. unsub-neg 73.1%

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

   6. Simplified 73.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.6 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.2e-57)
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
   (if (<= C 2.7e-18)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e-57) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 2.7e-18) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e-57) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else if (C <= 2.7e-18) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.2e-57:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	elif C <= 2.7e-18:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.2e-57)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	elseif (C <= 2.7e-18)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / 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 <= -1.2e-57)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	elseif (C <= 2.7e-18)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.2e-57], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.7e-18], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $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 < -1.20000000000000003e-57

   1. Initial program 68.8%

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

   3. Taylor expanded in B around inf 79.1%

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

   4. Taylor expanded in A around 0 78.1%

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

   if -1.20000000000000003e-57 < C < 2.69999999999999989e-18

   1. Initial program 57.7%

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

   3. Taylor expanded in B around inf 50.6%

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

   4. Taylor expanded in C around 0 49.8%

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

      1. neg-mul-1 49.8%

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

      2. distribute-neg-in 49.8%

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

      3. metadata-eval 49.8%

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

      4. unsub-neg 49.8%

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

   6. Simplified 49.8%

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

   if 2.69999999999999989e-18 < C

   1. Initial program 20.0%

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

   3. Taylor expanded in C around inf 69.0%

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

   4. Taylor expanded in B around inf 42.0%

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

      1. distribute-rgt1-in 42.0%

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

      2. metadata-eval 42.0%

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

      3. mul0-lft 42.0%

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

      4. div0 69.0%

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

      5. metadata-eval 69.0%

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

      6. neg-sub0 69.0%

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

      7. associate-*r/ 69.0%

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

      8. metadata-eval 69.0%

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

      9. distribute-neg-frac 69.0%

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

      10. metadata-eval 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -6.8 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.1 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -6.8e+99)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C 3.1e-20)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.8e+99) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 3.1e-20) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.8e+99) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 3.1e-20) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -6.8e+99:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 3.1e-20:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -6.8e+99)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 3.1e-20)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / 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 <= -6.8e+99)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 3.1e-20)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -6.8e+99], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.1e-20], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $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 < -6.79999999999999968e99

   1. Initial program 73.8%

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

   3. Taylor expanded in B around inf 76.2%

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

   4. Taylor expanded in C around inf 68.4%

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

   if -6.79999999999999968e99 < C < 3.1e-20

   1. Initial program 59.1%

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

   3. Taylor expanded in B around inf 58.6%

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

   4. Taylor expanded in C around 0 54.0%

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

      1. neg-mul-1 54.0%

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

      2. distribute-neg-in 54.0%

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

      3. metadata-eval 54.0%

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

      4. unsub-neg 54.0%

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

   6. Simplified 54.0%

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

   if 3.1e-20 < C

   1. Initial program 20.0%

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

   3. Taylor expanded in C around inf 69.0%

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

   4. Taylor expanded in B around inf 42.0%

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

      1. distribute-rgt1-in 42.0%

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

      2. metadata-eval 42.0%

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

      3. mul0-lft 42.0%

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

      4. div0 69.0%

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

      5. metadata-eval 69.0%

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

      6. neg-sub0 69.0%

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

      7. associate-*r/ 69.0%

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

      8. metadata-eval 69.0%

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

      9. distribute-neg-frac 69.0%

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

      10. metadata-eval 69.0%

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

   6. Simplified 69.0%

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

Alternative 17: 45.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.36 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-126}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.36e-103)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.18e-126)
     (/ (* 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 <= -1.36e-103) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.18e-126) {
		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 <= -1.36e-103) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.18e-126) {
		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 <= -1.36e-103:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.18e-126:
		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 <= -1.36e-103)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.18e-126)
		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 <= -1.36e-103)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.18e-126)
		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, -1.36e-103], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.18e-126], 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 < -1.36000000000000006e-103

   1. Initial program 49.5%

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

   3. Taylor expanded in B around -inf 58.6%

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

   if -1.36000000000000006e-103 < B < 1.1799999999999999e-126

   1. Initial program 51.0%

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

      1. associate-*r/ 50.9%

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

   4. Applied egg-rr 79.5%

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

   5. Taylor expanded in C around inf 37.0%

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

      1. distribute-rgt1-in 37.0%

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

      2. metadata-eval 37.0%

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

      3. mul0-lft 37.0%

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

      4. div0 37.0%

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

      5. metadata-eval 37.0%

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

   7. Simplified 37.0%

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

   if 1.1799999999999999e-126 < B

   1. Initial program 55.8%

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

   3. Taylor expanded in B around inf 54.3%

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

Alternative 18: 39.8% 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 52.9%

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

   3. Taylor expanded in B around -inf 41.0%

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

   if -4.999999999999985e-310 < B

   1. Initial program 51.9%

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

   3. Taylor expanded in B around inf 42.0%

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

Alternative 19: 21.6% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.4%

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

3. Taylor expanded in B around inf 22.9%

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

Reproduce

herbie shell --seed 2024136 
(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)))