ABCF->ab-angle angle

Percentage Accurate: 54.1% → 82.0%

Time: 20.8s

Alternatives: 23

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: 54.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.2e+106)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+106) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+106) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.2e+106:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.2e+106)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.2e+106)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.2e+106], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.1999999999999998e106

   1. Initial program 14.3%

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

      1. associate-*r/ 14.3%

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

      2. associate-*l/ 14.3%

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

      3. *-un-lft-identity 14.3%

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

      4. unpow2 14.3%

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

      5. unpow2 14.3%

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

      6. hypot-define 45.6%

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

   4. Applied egg-rr 45.6%

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

   5. Taylor expanded in A around -inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. distribute-lft-out 87.8%

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

      3. associate-*r* 87.8%

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

      4. metadata-eval 87.8%

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

      5. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

   if -3.1999999999999998e106 < A

   1. Initial program 61.6%

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

      1. associate-*l/ 61.6%

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

      2. *-lft-identity 61.6%

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

      3. +-commutative 61.6%

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

      4. unpow2 61.6%

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

      5. unpow2 61.6%

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

      6. hypot-define 85.4%

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

   3. Simplified 85.4%

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

Alternative 2: 78.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.02 \cdot 10^{+108}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.02e+108)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 5.6e-68)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.02e+108) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 5.6e-68) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.02e+108) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 5.6e-68) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.02e+108:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 5.6e-68:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.02e+108)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 5.6e-68)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.02e+108)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 5.6e-68)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.02e+108], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.6e-68], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.02e108

   1. Initial program 14.3%

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

      1. associate-*r/ 14.3%

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

      2. associate-*l/ 14.3%

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

      3. *-un-lft-identity 14.3%

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

      4. unpow2 14.3%

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

      5. unpow2 14.3%

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

      6. hypot-define 45.6%

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

   4. Applied egg-rr 45.6%

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

   5. Taylor expanded in A around -inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. distribute-lft-out 87.8%

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

      3. associate-*r* 87.8%

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

      4. metadata-eval 87.8%

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

      5. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

   if -1.02e108 < A < 5.6000000000000002e-68

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 83.3%

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

   4. Applied egg-rr 83.3%

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

   5. Taylor expanded in A around 0 54.4%

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

      1. unpow2 54.4%

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

      2. unpow2 54.4%

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

      3. hypot-define 80.7%

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

   7. Simplified 80.7%

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

   if 5.6000000000000002e-68 < A

   1. Initial program 69.4%

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

   3. Taylor expanded in C around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-neg-frac2 68.4%

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

      3. +-commutative 68.4%

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

      4. unpow2 68.4%

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

      5. unpow2 68.4%

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

      6. hypot-define 79.9%

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

   5. Simplified 79.9%

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

Alternative 3: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.4 \cdot 10^{+50}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+106)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 7.4e+50)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+106) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 7.4e+50) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+106) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 7.4e+50) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+106:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 7.4e+50:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+106)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 7.4e+50)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+106)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 7.4e+50)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+106], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 7.4e+50], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.70000000000000006e106

   1. Initial program 14.3%

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

      1. associate-*r/ 14.3%

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

      2. associate-*l/ 14.3%

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

      3. *-un-lft-identity 14.3%

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

      4. unpow2 14.3%

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

      5. unpow2 14.3%

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

      6. hypot-define 45.6%

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

   4. Applied egg-rr 45.6%

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

   5. Taylor expanded in A around -inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. distribute-lft-out 87.8%

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

      3. associate-*r* 87.8%

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

      4. metadata-eval 87.8%

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

      5. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

   if -2.70000000000000006e106 < A < 7.4000000000000001e50

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 82.8%

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

   4. Applied egg-rr 82.8%

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

   5. Taylor expanded in A around 0 52.8%

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

      1. unpow2 52.8%

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

      2. unpow2 52.8%

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

      3. hypot-define 78.5%

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

   7. Simplified 78.5%

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

   if 7.4000000000000001e50 < A

   1. Initial program 74.5%

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

   3. Taylor expanded in B around inf 81.0%

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

   4. Taylor expanded in B around 0 81.0%

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

      1. associate--r+ 81.0%

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

      2. sub-neg 81.0%

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

      3. mul-1-neg 81.0%

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

      4. mul-1-neg 81.0%

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

      5. sub-neg 81.0%

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

      6. div-sub 81.0%

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

      7. sub-neg 81.0%

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

      8. *-inverses 81.0%

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

      9. metadata-eval 81.0%

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

   6. Simplified 81.0%

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

Alternative 4: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e+107)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 1.1e+51)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 1.1e+51) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 1.1e+51) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 1.1e+51:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 1.1e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 1.1e+51)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e+107], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.1e+51], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.15e107

   1. Initial program 14.3%

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

      1. associate-*r/ 14.3%

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

      2. associate-*l/ 14.3%

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

      3. *-un-lft-identity 14.3%

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

      4. unpow2 14.3%

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

      5. unpow2 14.3%

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

      6. hypot-define 45.6%

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

   4. Applied egg-rr 45.6%

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

   5. Taylor expanded in A around -inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. distribute-lft-out 87.8%

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

      3. associate-*r* 87.8%

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

      4. metadata-eval 87.8%

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

      5. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

   if -1.15e107 < A < 1.09999999999999996e51

   1. Initial program 57.1%

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

   3. Taylor expanded in A around 0 52.8%

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

      1. unpow2 52.8%

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

      2. unpow2 52.8%

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

      3. hypot-define 78.5%

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

   5. Simplified 78.5%

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

   if 1.09999999999999996e51 < A

   1. Initial program 74.5%

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

   3. Taylor expanded in B around inf 81.0%

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

   4. Taylor expanded in B around 0 81.0%

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

      1. associate--r+ 81.0%

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

      2. sub-neg 81.0%

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

      3. mul-1-neg 81.0%

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

      4. mul-1-neg 81.0%

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

      5. sub-neg 81.0%

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

      6. div-sub 81.0%

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

      7. sub-neg 81.0%

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

      8. *-inverses 81.0%

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

      9. metadata-eval 81.0%

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

   6. Simplified 81.0%

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

Alternative 5: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e+100)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+100) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+100) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e+100:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e+100)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e+100)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e+100], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.50000000000000043e100

   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%

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

      2. associate-*l/ 16.3%

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

      3. *-un-lft-identity 16.3%

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

      4. unpow2 16.3%

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

      5. unpow2 16.3%

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

      6. hypot-define 46.9%

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

   4. Applied egg-rr 46.9%

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

   5. Taylor expanded in A around -inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. distribute-lft-out 88.1%

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

      3. associate-*r* 88.1%

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

      4. metadata-eval 88.1%

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

      5. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

   if -8.50000000000000043e100 < A

   1. Initial program 61.4%

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

   3. Simplified 84.9%

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

Alternative 6: 64.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.1 \cdot 10^{-230}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-302}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot \left(-1 - 0.5 \cdot \frac{A}{B}\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-116}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.1e-230)
   (* 180.0 (/ (atan (* (/ 1.0 B) (+ B (- C A)))) PI))
   (if (<= B 1.95e-302)
     (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
     (if (<= B 7.8e-244)
       (* 180.0 (/ (atan (/ (- (* A (- -1.0 (* 0.5 (/ A B)))) B) B)) PI))
       (if (<= B 3.5e-230)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 4.6e-116)
           (/ (* 180.0 (atan (+ (/ (- C A) B) -1.0))) PI)
           (if (<= B 3.4e-75)
             (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
             (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.1e-230) {
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / ((double) M_PI));
	} else if (B <= 1.95e-302) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (B <= 7.8e-244) {
		tmp = 180.0 * (atan((((A * (-1.0 - (0.5 * (A / B)))) - B) / B)) / ((double) M_PI));
	} else if (B <= 3.5e-230) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 4.6e-116) {
		tmp = (180.0 * atan((((C - A) / B) + -1.0))) / ((double) M_PI);
	} else if (B <= 3.4e-75) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.1e-230) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (B + (C - A)))) / Math.PI);
	} else if (B <= 1.95e-302) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (B <= 7.8e-244) {
		tmp = 180.0 * (Math.atan((((A * (-1.0 - (0.5 * (A / B)))) - B) / B)) / Math.PI);
	} else if (B <= 3.5e-230) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 4.6e-116) {
		tmp = (180.0 * Math.atan((((C - A) / B) + -1.0))) / Math.PI;
	} else if (B <= 3.4e-75) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.1e-230:
		tmp = 180.0 * (math.atan(((1.0 / B) * (B + (C - A)))) / math.pi)
	elif B <= 1.95e-302:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif B <= 7.8e-244:
		tmp = 180.0 * (math.atan((((A * (-1.0 - (0.5 * (A / B)))) - B) / B)) / math.pi)
	elif B <= 3.5e-230:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 4.6e-116:
		tmp = (180.0 * math.atan((((C - A) / B) + -1.0))) / math.pi
	elif B <= 3.4e-75:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.1e-230)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B + Float64(C - A)))) / pi));
	elseif (B <= 1.95e-302)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (B <= 7.8e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(A * Float64(-1.0 - Float64(0.5 * Float64(A / B)))) - B) / B)) / pi));
	elseif (B <= 3.5e-230)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 4.6e-116)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) / B) + -1.0))) / pi);
	elseif (B <= 3.4e-75)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.1e-230)
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / pi);
	elseif (B <= 1.95e-302)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (B <= 7.8e-244)
		tmp = 180.0 * (atan((((A * (-1.0 - (0.5 * (A / B)))) - B) / B)) / pi);
	elseif (B <= 3.5e-230)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 4.6e-116)
		tmp = (180.0 * atan((((C - A) / B) + -1.0))) / pi;
	elseif (B <= 3.4e-75)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.1e-230], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B + N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-302], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.8e-244], N[(180.0 * N[(N[ArcTan[N[(N[(N[(A * N[(-1.0 - N[(0.5 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e-230], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 4.6e-116], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.4e-75], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -5.0999999999999999e-230

   1. Initial program 53.0%

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

   3. Taylor expanded in B around -inf 70.0%

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

      1. neg-mul-1 70.0%

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

   5. Simplified 70.0%

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

   if -5.0999999999999999e-230 < B < 1.95e-302

   1. Initial program 62.1%

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

      1. associate-*r/ 62.1%

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

      2. associate-*l/ 62.1%

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

      3. *-un-lft-identity 62.1%

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

      4. unpow2 62.1%

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

      5. unpow2 62.1%

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

      6. hypot-define 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in A around -inf 61.6%

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

      1. associate-*r/ 61.6%

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

      2. distribute-lft-out 61.6%

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

      3. associate-*r* 61.6%

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

      4. metadata-eval 61.6%

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

      5. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if 1.95e-302 < B < 7.7999999999999998e-244

   1. Initial program 75.9%

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

   3. Taylor expanded in C around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-neg-frac2 63.6%

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

      3. +-commutative 63.6%

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

      4. unpow2 63.6%

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

      5. unpow2 63.6%

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

      6. hypot-define 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in A around 0 76.1%

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

   if 7.7999999999999998e-244 < B < 3.49999999999999988e-230

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 3.49999999999999988e-230 < B < 4.60000000000000003e-116

   1. Initial program 62.7%

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

      1. associate-*r/ 62.7%

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

      2. associate-*l/ 62.6%

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

      3. *-un-lft-identity 62.6%

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

      4. unpow2 62.6%

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

      5. unpow2 62.6%

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

      6. hypot-define 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in B around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. associate--r+ 48.6%

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

      3. div-sub 59.9%

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

      4. sub-neg 59.9%

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

      5. metadata-eval 59.9%

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

   7. Simplified 59.9%

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

   if 4.60000000000000003e-116 < B < 3.40000000000000015e-75

   1. Initial program 19.4%

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

      1. associate-*r/ 19.4%

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

      2. associate-*l/ 19.4%

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

      3. *-un-lft-identity 19.4%

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

      4. unpow2 19.4%

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

      5. unpow2 19.4%

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

      6. hypot-define 60.8%

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

   4. Applied egg-rr 60.8%

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

   5. Taylor expanded in A around -inf 60.0%

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

      1. associate-*r/ 60.0%

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

   7. Simplified 60.0%

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

   if 3.40000000000000015e-75 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 77.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.1 \cdot 10^{-230}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-302}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot \left(-1 - 0.5 \cdot \frac{A}{B}\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-116}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{if}\;B \leq -9 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-299}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-244}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-118}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))
   (if (<= B -9e-229)
     (* 180.0 (/ (atan (* (/ 1.0 B) (+ B (- C A)))) PI))
     (if (<= B 2.35e-299)
       (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
       (if (<= B 7.2e-244)
         t_0
         (if (<= B 2.55e-231)
           (/ (* 180.0 (atan 0.0)) PI)
           (if (<= B 8e-118)
             (/ (* 180.0 (atan (+ (/ (- C A) B) -1.0))) PI)
             (if (<= B 3.4e-75)
               (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
               t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	double tmp;
	if (B <= -9e-229) {
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / ((double) M_PI));
	} else if (B <= 2.35e-299) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (B <= 7.2e-244) {
		tmp = t_0;
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 8e-118) {
		tmp = (180.0 * atan((((C - A) / B) + -1.0))) / ((double) M_PI);
	} else if (B <= 3.4e-75) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	double tmp;
	if (B <= -9e-229) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (B + (C - A)))) / Math.PI);
	} else if (B <= 2.35e-299) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (B <= 7.2e-244) {
		tmp = t_0;
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 8e-118) {
		tmp = (180.0 * Math.atan((((C - A) / B) + -1.0))) / Math.PI;
	} else if (B <= 3.4e-75) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	tmp = 0
	if B <= -9e-229:
		tmp = 180.0 * (math.atan(((1.0 / B) * (B + (C - A)))) / math.pi)
	elif B <= 2.35e-299:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif B <= 7.2e-244:
		tmp = t_0
	elif B <= 2.55e-231:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 8e-118:
		tmp = (180.0 * math.atan((((C - A) / B) + -1.0))) / math.pi
	elif B <= 3.4e-75:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi))
	tmp = 0.0
	if (B <= -9e-229)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B + Float64(C - A)))) / pi));
	elseif (B <= 2.35e-299)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (B <= 7.2e-244)
		tmp = t_0;
	elseif (B <= 2.55e-231)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 8e-118)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) / B) + -1.0))) / pi);
	elseif (B <= 3.4e-75)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	tmp = 0.0;
	if (B <= -9e-229)
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / pi);
	elseif (B <= 2.35e-299)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (B <= 7.2e-244)
		tmp = t_0;
	elseif (B <= 2.55e-231)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 8e-118)
		tmp = (180.0 * atan((((C - A) / B) + -1.0))) / pi;
	elseif (B <= 3.4e-75)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9e-229], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B + N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.35e-299], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.2e-244], t$95$0, If[LessEqual[B, 2.55e-231], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8e-118], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.4e-75], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -9.0000000000000004e-229

   1. Initial program 53.0%

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

   3. Taylor expanded in B around -inf 70.0%

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

      1. neg-mul-1 70.0%

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

   5. Simplified 70.0%

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

   if -9.0000000000000004e-229 < B < 2.3499999999999999e-299

   1. Initial program 62.1%

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

      1. associate-*r/ 62.1%

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

      2. associate-*l/ 62.1%

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

      3. *-un-lft-identity 62.1%

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

      4. unpow2 62.1%

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

      5. unpow2 62.1%

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

      6. hypot-define 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in A around -inf 61.6%

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

      1. associate-*r/ 61.6%

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

      2. distribute-lft-out 61.6%

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

      3. associate-*r* 61.6%

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

      4. metadata-eval 61.6%

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

      5. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if 2.3499999999999999e-299 < B < 7.1999999999999995e-244 or 3.40000000000000015e-75 < B

   1. Initial program 56.8%

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

   3. Taylor expanded in B around inf 77.6%

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

   if 7.1999999999999995e-244 < B < 2.55e-231

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 2.55e-231 < B < 7.99999999999999988e-118

   1. Initial program 62.7%

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

      1. associate-*r/ 62.7%

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

      2. associate-*l/ 62.6%

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

      3. *-un-lft-identity 62.6%

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

      4. unpow2 62.6%

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

      5. unpow2 62.6%

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

      6. hypot-define 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in B around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. associate--r+ 48.6%

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

      3. div-sub 59.9%

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

      4. sub-neg 59.9%

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

      5. metadata-eval 59.9%

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

   7. Simplified 59.9%

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

   if 7.99999999999999988e-118 < B < 3.40000000000000015e-75

   1. Initial program 19.4%

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

      1. associate-*r/ 19.4%

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

      2. associate-*l/ 19.4%

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

      3. *-un-lft-identity 19.4%

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

      4. unpow2 19.4%

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

      5. unpow2 19.4%

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

      6. hypot-define 60.8%

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

   4. Applied egg-rr 60.8%

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

   5. Taylor expanded in A around -inf 60.0%

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

      1. associate-*r/ 60.0%

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

   7. Simplified 60.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-299}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-118}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := \tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;C \leq -3.5 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-280}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* (atan (- -1.0 (/ A B))) (/ 180.0 PI))))
   (if (<= C -3.5e-95)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= C 2.1e-280)
       (* 180.0 (/ (atan (/ (- B A) B)) PI))
       (if (<= C 4.4e-91)
         t_1
         (if (<= C 3.5e-61)
           t_0
           (if (<= C 2.6e-45)
             (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
             (if (<= C 1.1e+47) t_1 t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double t_1 = atan((-1.0 - (A / B))) * (180.0 / ((double) M_PI));
	double tmp;
	if (C <= -3.5e-95) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 2.1e-280) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else if (C <= 4.4e-91) {
		tmp = t_1;
	} else if (C <= 3.5e-61) {
		tmp = t_0;
	} else if (C <= 2.6e-45) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 1.1e+47) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double t_1 = Math.atan((-1.0 - (A / B))) * (180.0 / Math.PI);
	double tmp;
	if (C <= -3.5e-95) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 2.1e-280) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else if (C <= 4.4e-91) {
		tmp = t_1;
	} else if (C <= 3.5e-61) {
		tmp = t_0;
	} else if (C <= 2.6e-45) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 1.1e+47) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	t_1 = math.atan((-1.0 - (A / B))) * (180.0 / math.pi)
	tmp = 0
	if C <= -3.5e-95:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 2.1e-280:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	elif C <= 4.4e-91:
		tmp = t_1
	elif C <= 3.5e-61:
		tmp = t_0
	elif C <= 2.6e-45:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 1.1e+47:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	t_1 = Float64(atan(Float64(-1.0 - Float64(A / B))) * Float64(180.0 / pi))
	tmp = 0.0
	if (C <= -3.5e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 2.1e-280)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	elseif (C <= 4.4e-91)
		tmp = t_1;
	elseif (C <= 3.5e-61)
		tmp = t_0;
	elseif (C <= 2.6e-45)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 1.1e+47)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	t_1 = atan((-1.0 - (A / B))) * (180.0 / pi);
	tmp = 0.0;
	if (C <= -3.5e-95)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 2.1e-280)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	elseif (C <= 4.4e-91)
		tmp = t_1;
	elseif (C <= 3.5e-61)
		tmp = t_0;
	elseif (C <= 2.6e-45)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 1.1e+47)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -3.5e-95], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e-280], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.4e-91], t$95$1, If[LessEqual[C, 3.5e-61], t$95$0, If[LessEqual[C, 2.6e-45], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.1e+47], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -3.4999999999999997e-95

   1. Initial program 70.1%

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

   3. Taylor expanded in B around inf 72.7%

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

   4. Taylor expanded in A around 0 70.1%

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

   if -3.4999999999999997e-95 < C < 2.10000000000000001e-280

   1. Initial program 63.8%

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

   3. Taylor expanded in B around -inf 60.3%

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

      1. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in C around 0 58.5%

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

   if 2.10000000000000001e-280 < C < 4.4000000000000002e-91 or 2.59999999999999987e-45 < C < 1.1e47

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-un-lft-identity 51.8%

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

      4. unpow2 51.8%

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

      5. unpow2 51.8%

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

      6. hypot-define 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in B around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. associate--r+ 55.5%

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

      3. div-sub 55.5%

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

      4. sub-neg 55.5%

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

      5. metadata-eval 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in C around 0 55.6%

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

      1. distribute-lft-in 55.6%

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

      2. metadata-eval 55.6%

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

      3. mul-1-neg 55.6%

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

      4. unsub-neg 55.6%

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

   10. Simplified 55.6%

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

   11. Taylor expanded in A around 0 55.6%

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

       1. associate-*r/ 55.6%

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

       2. *-commutative 55.6%

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

       3. +-commutative 55.6%

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

       4. distribute-neg-in 55.6%

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

       5. neg-mul-1 55.6%

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

       6. sub-neg 55.6%

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

       7. sub-neg 55.6%

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

       8. metadata-eval 55.6%

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

       9. +-commutative 55.6%

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

       10. neg-mul-1 55.6%

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

       11. sub-neg 55.6%

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

       12. associate-/l* 55.6%

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

   13. Simplified 55.6%

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

   if 4.4000000000000002e-91 < C < 3.5000000000000003e-61 or 1.1e47 < C

   1. Initial program 22.3%

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

   3. Taylor expanded in C around inf 70.7%

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

   4. Taylor expanded in A around inf 70.7%

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

   if 3.5000000000000003e-61 < C < 2.59999999999999987e-45

   1. Initial program 61.3%

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

   3. Taylor expanded in A around -inf 83.4%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

Alternative 9: 55.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -390000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-261}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ B C) B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))))
   (if (<= A -2.3e+94)
     t_1
     (if (<= A -390000000.0)
       t_0
       (if (<= A -6e-70)
         t_1
         (if (<= A -1.25e-261)
           t_0
           (if (<= A 6.5e-296)
             (* 180.0 (/ (atan -1.0) PI))
             (if (<= A 1.2e-26)
               t_0
               (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -2.3e+94) {
		tmp = t_1;
	} else if (A <= -390000000.0) {
		tmp = t_0;
	} else if (A <= -6e-70) {
		tmp = t_1;
	} else if (A <= -1.25e-261) {
		tmp = t_0;
	} else if (A <= 6.5e-296) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.2e-26) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	double tmp;
	if (A <= -2.3e+94) {
		tmp = t_1;
	} else if (A <= -390000000.0) {
		tmp = t_0;
	} else if (A <= -6e-70) {
		tmp = t_1;
	} else if (A <= -1.25e-261) {
		tmp = t_0;
	} else if (A <= 6.5e-296) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.2e-26) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	t_1 = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	tmp = 0
	if A <= -2.3e+94:
		tmp = t_1
	elif A <= -390000000.0:
		tmp = t_0
	elif A <= -6e-70:
		tmp = t_1
	elif A <= -1.25e-261:
		tmp = t_0
	elif A <= 6.5e-296:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.2e-26:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi))
	tmp = 0.0
	if (A <= -2.3e+94)
		tmp = t_1;
	elseif (A <= -390000000.0)
		tmp = t_0;
	elseif (A <= -6e-70)
		tmp = t_1;
	elseif (A <= -1.25e-261)
		tmp = t_0;
	elseif (A <= 6.5e-296)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.2e-26)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B + C) / B)) / pi);
	t_1 = 180.0 * (atan(((0.5 * B) / A)) / pi);
	tmp = 0.0;
	if (A <= -2.3e+94)
		tmp = t_1;
	elseif (A <= -390000000.0)
		tmp = t_0;
	elseif (A <= -6e-70)
		tmp = t_1;
	elseif (A <= -1.25e-261)
		tmp = t_0;
	elseif (A <= 6.5e-296)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.2e-26)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.3e+94], t$95$1, If[LessEqual[A, -390000000.0], t$95$0, If[LessEqual[A, -6e-70], t$95$1, If[LessEqual[A, -1.25e-261], t$95$0, If[LessEqual[A, 6.5e-296], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.2e-26], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.3e94 or -3.9e8 < A < -6.0000000000000003e-70

   1. Initial program 21.1%

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

   3. Taylor expanded in A around -inf 77.7%

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

      1. associate-*r/ 77.7%

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

   5. Simplified 77.7%

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

   if -2.3e94 < A < -3.9e8 or -6.0000000000000003e-70 < A < -1.24999999999999995e-261 or 6.49999999999999963e-296 < A < 1.2e-26

   1. Initial program 59.0%

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

   3. Taylor expanded in B around -inf 55.8%

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

      1. neg-mul-1 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in A around 0 53.2%

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

   if -1.24999999999999995e-261 < A < 6.49999999999999963e-296

   1. Initial program 57.5%

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

   3. Taylor expanded in B around inf 64.2%

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

   if 1.2e-26 < A

   1. Initial program 71.7%

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

   3. Taylor expanded in A around inf 63.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -390000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-294}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= A -6.5e-239)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (if (<= A 1.22e-294)
       t_0
       (if (<= A 2.6e-250)
         (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
         (if (<= A 1.3e-208)
           t_0
           (if (<= A 6.5e-31)
             (* 180.0 (/ (atan 1.0) PI))
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (A <= -6.5e-239) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.22e-294) {
		tmp = t_0;
	} else if (A <= 2.6e-250) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (A <= 1.3e-208) {
		tmp = t_0;
	} else if (A <= 6.5e-31) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (A <= -6.5e-239) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.22e-294) {
		tmp = t_0;
	} else if (A <= 2.6e-250) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (A <= 1.3e-208) {
		tmp = t_0;
	} else if (A <= 6.5e-31) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if A <= -6.5e-239:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.22e-294:
		tmp = t_0
	elif A <= 2.6e-250:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif A <= 1.3e-208:
		tmp = t_0
	elif A <= 6.5e-31:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (A <= -6.5e-239)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.22e-294)
		tmp = t_0;
	elseif (A <= 2.6e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (A <= 1.3e-208)
		tmp = t_0;
	elseif (A <= 6.5e-31)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (A <= -6.5e-239)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.22e-294)
		tmp = t_0;
	elseif (A <= 2.6e-250)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (A <= 1.3e-208)
		tmp = t_0;
	elseif (A <= 6.5e-31)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -6.5e-239], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.22e-294], t$95$0, If[LessEqual[A, 2.6e-250], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.3e-208], t$95$0, If[LessEqual[A, 6.5e-31], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -6.5000000000000003e-239

   1. Initial program 38.0%

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

   3. Taylor expanded in A around -inf 53.2%

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

      1. associate-*r/ 53.2%

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

   5. Simplified 53.2%

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

   if -6.5000000000000003e-239 < A < 1.21999999999999995e-294 or 2.60000000000000008e-250 < A < 1.30000000000000008e-208

   1. Initial program 55.7%

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

   3. Taylor expanded in B around inf 54.8%

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

   if 1.21999999999999995e-294 < A < 2.60000000000000008e-250

   1. Initial program 82.3%

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

   3. Taylor expanded in C around -inf 61.3%

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

   if 1.30000000000000008e-208 < A < 6.49999999999999967e-31

   1. Initial program 63.2%

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

   3. Taylor expanded in B around -inf 40.5%

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

   if 6.49999999999999967e-31 < A

   1. Initial program 71.7%

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

   3. Taylor expanded in A around inf 63.9%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{if}\;B \leq 8.6 \cdot 10^{-244}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))))
   (if (<= B 8.6e-244)
     t_0
     (if (<= B 2.6e-231)
       (/ (* 180.0 (atan 0.0)) PI)
       (if (<= B 8.2e-118)
         t_0
         (if (<= B 3.8e-75)
           (/ (* 180.0 (atan (/ (* 0.5 B) A))) PI)
           (* (atan (- -1.0 (/ A B))) (/ 180.0 PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	double tmp;
	if (B <= 8.6e-244) {
		tmp = t_0;
	} else if (B <= 2.6e-231) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 8.2e-118) {
		tmp = t_0;
	} else if (B <= 3.8e-75) {
		tmp = (180.0 * atan(((0.5 * B) / A))) / ((double) M_PI);
	} else {
		tmp = atan((-1.0 - (A / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	double tmp;
	if (B <= 8.6e-244) {
		tmp = t_0;
	} else if (B <= 2.6e-231) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 8.2e-118) {
		tmp = t_0;
	} else if (B <= 3.8e-75) {
		tmp = (180.0 * Math.atan(((0.5 * B) / A))) / Math.PI;
	} else {
		tmp = Math.atan((-1.0 - (A / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	tmp = 0
	if B <= 8.6e-244:
		tmp = t_0
	elif B <= 2.6e-231:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 8.2e-118:
		tmp = t_0
	elif B <= 3.8e-75:
		tmp = (180.0 * math.atan(((0.5 * B) / A))) / math.pi
	else:
		tmp = math.atan((-1.0 - (A / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi))
	tmp = 0.0
	if (B <= 8.6e-244)
		tmp = t_0;
	elseif (B <= 2.6e-231)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 8.2e-118)
		tmp = t_0;
	elseif (B <= 3.8e-75)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * B) / A))) / pi);
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(A / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	tmp = 0.0;
	if (B <= 8.6e-244)
		tmp = t_0;
	elseif (B <= 2.6e-231)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 8.2e-118)
		tmp = t_0;
	elseif (B <= 3.8e-75)
		tmp = (180.0 * atan(((0.5 * B) / A))) / pi;
	else
		tmp = atan((-1.0 - (A / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 8.6e-244], t$95$0, If[LessEqual[B, 2.6e-231], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.2e-118], t$95$0, If[LessEqual[B, 3.8e-75], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < 8.59999999999999973e-244 or 2.60000000000000003e-231 < B < 8.2000000000000006e-118

   1. Initial program 56.8%

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

   3. Taylor expanded in B around -inf 62.0%

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

      1. associate--l+ 62.0%

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

      2. div-sub 64.8%

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

   5. Simplified 64.8%

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

   if 8.59999999999999973e-244 < B < 2.60000000000000003e-231

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 8.2000000000000006e-118 < B < 3.79999999999999994e-75

   1. Initial program 19.4%

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

      1. associate-*r/ 19.4%

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

      2. associate-*l/ 19.4%

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

      3. *-un-lft-identity 19.4%

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

      4. unpow2 19.4%

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

      5. unpow2 19.4%

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

      6. hypot-define 60.8%

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

   4. Applied egg-rr 60.8%

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

   5. Taylor expanded in A around -inf 60.0%

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

      1. associate-*r/ 60.0%

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

   7. Simplified 60.0%

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

   if 3.79999999999999994e-75 < B

   1. Initial program 55.1%

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

      1. associate-*r/ 55.1%

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

      2. associate-*l/ 55.1%

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

      3. *-un-lft-identity 55.1%

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

      4. unpow2 55.1%

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

      5. unpow2 55.1%

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

      6. hypot-define 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in B around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. associate--r+ 77.7%

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

      3. div-sub 77.7%

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

      4. sub-neg 77.7%

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

      5. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in C around 0 69.5%

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

      1. distribute-lft-in 69.5%

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

      2. metadata-eval 69.5%

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

      3. mul-1-neg 69.5%

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

      4. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

   11. Taylor expanded in A around 0 69.5%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. +-commutative 69.5%

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

       4. distribute-neg-in 69.5%

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

       5. neg-mul-1 69.5%

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

       6. sub-neg 69.5%

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

       7. sub-neg 69.5%

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

       8. metadata-eval 69.5%

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

       9. +-commutative 69.5%

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

       10. neg-mul-1 69.5%

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

       11. sub-neg 69.5%

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

       12. associate-/l* 69.5%

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

   13. Simplified 69.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 8.6 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{if}\;B \leq -1.6 \cdot 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-256}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (* 0.5 B) A))))
   (if (<= B -1.6e-236)
     (* 180.0 (/ (atan (/ (- B A) B)) PI))
     (if (<= B -1.25e-256)
       (/ (* 180.0 t_0) PI)
       (if (<= B 8e-285)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (if (<= B 7.2e-74)
           (* 180.0 (/ t_0 PI))
           (* (atan (- -1.0 (/ A B))) (/ 180.0 PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A));
	double tmp;
	if (B <= -1.6e-236) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else if (B <= -1.25e-256) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else if (B <= 8e-285) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 7.2e-74) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else {
		tmp = atan((-1.0 - (A / B))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A));
	double tmp;
	if (B <= -1.6e-236) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else if (B <= -1.25e-256) {
		tmp = (180.0 * t_0) / Math.PI;
	} else if (B <= 8e-285) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 7.2e-74) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else {
		tmp = Math.atan((-1.0 - (A / B))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A))
	tmp = 0
	if B <= -1.6e-236:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	elif B <= -1.25e-256:
		tmp = (180.0 * t_0) / math.pi
	elif B <= 8e-285:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 7.2e-74:
		tmp = 180.0 * (t_0 / math.pi)
	else:
		tmp = math.atan((-1.0 - (A / B))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(0.5 * B) / A))
	tmp = 0.0
	if (B <= -1.6e-236)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	elseif (B <= -1.25e-256)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	elseif (B <= 8e-285)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 7.2e-74)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	else
		tmp = Float64(atan(Float64(-1.0 - Float64(A / B))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A));
	tmp = 0.0;
	if (B <= -1.6e-236)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	elseif (B <= -1.25e-256)
		tmp = (180.0 * t_0) / pi;
	elseif (B <= 8e-285)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 7.2e-74)
		tmp = 180.0 * (t_0 / pi);
	else
		tmp = atan((-1.0 - (A / B))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[B, -1.6e-236], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.25e-256], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8e-285], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-74], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.6e-236

   1. Initial program 53.0%

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

   3. Taylor expanded in B around -inf 69.6%

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

      1. neg-mul-1 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in C around 0 60.6%

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

   if -1.6e-236 < B < -1.25e-256

   1. Initial program 48.7%

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

      1. associate-*r/ 48.7%

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

      2. associate-*l/ 48.7%

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

      3. *-un-lft-identity 48.7%

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

      4. unpow2 48.7%

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

      5. unpow2 48.7%

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

      6. hypot-define 81.0%

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

   4. Applied egg-rr 81.0%

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

   5. Taylor expanded in A around -inf 82.2%

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

      1. associate-*r/ 82.2%

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

   7. Simplified 82.2%

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

   if -1.25e-256 < B < 8.00000000000000059e-285

   1. Initial program 75.2%

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

   3. Taylor expanded in B around inf 64.2%

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

   4. Taylor expanded in A around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. mul-1-neg 59.0%

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

   6. Simplified 59.0%

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

   if 8.00000000000000059e-285 < B < 7.2000000000000005e-74

   1. Initial program 45.6%

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

   3. Taylor expanded in A around -inf 44.7%

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

      1. associate-*r/ 44.7%

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

   5. Simplified 44.7%

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

   if 7.2000000000000005e-74 < B

   1. Initial program 55.1%

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

      1. associate-*r/ 55.1%

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

      2. associate-*l/ 55.1%

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

      3. *-un-lft-identity 55.1%

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

      4. unpow2 55.1%

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

      5. unpow2 55.1%

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

      6. hypot-define 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in B around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. associate--r+ 77.7%

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

      3. div-sub 77.7%

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

      4. sub-neg 77.7%

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

      5. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in C around 0 69.5%

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

      1. distribute-lft-in 69.5%

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

      2. metadata-eval 69.5%

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

      3. mul-1-neg 69.5%

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

      4. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

   11. Taylor expanded in A around 0 69.5%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. +-commutative 69.5%

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

       4. distribute-neg-in 69.5%

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

       5. neg-mul-1 69.5%

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

       6. sub-neg 69.5%

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

       7. sub-neg 69.5%

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

       8. metadata-eval 69.5%

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

       9. +-commutative 69.5%

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

       10. neg-mul-1 69.5%

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

       11. sub-neg 69.5%

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

       12. associate-/l* 69.5%

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

   13. Simplified 69.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-256}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -7.4 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-229}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- B A) B)) PI))))
   (if (<= C -7.4e-95)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= C 2.2e-229)
       t_0
       (if (<= C 1.2e-47)
         (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
         (if (<= C 1.75e-7) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	double tmp;
	if (C <= -7.4e-95) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 2.2e-229) {
		tmp = t_0;
	} else if (C <= 1.2e-47) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 1.75e-7) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	double tmp;
	if (C <= -7.4e-95) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 2.2e-229) {
		tmp = t_0;
	} else if (C <= 1.2e-47) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 1.75e-7) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	tmp = 0
	if C <= -7.4e-95:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 2.2e-229:
		tmp = t_0
	elif C <= 1.2e-47:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 1.75e-7:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi))
	tmp = 0.0
	if (C <= -7.4e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 2.2e-229)
		tmp = t_0;
	elseif (C <= 1.2e-47)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 1.75e-7)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B - A) / B)) / pi);
	tmp = 0.0;
	if (C <= -7.4e-95)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 2.2e-229)
		tmp = t_0;
	elseif (C <= 1.2e-47)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 1.75e-7)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7.4e-95], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.2e-229], t$95$0, If[LessEqual[C, 1.2e-47], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.75e-7], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -7.39999999999999989e-95

   1. Initial program 70.1%

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

   3. Taylor expanded in B around inf 72.7%

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

   4. Taylor expanded in A around 0 70.1%

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

   if -7.39999999999999989e-95 < C < 2.1999999999999999e-229 or 1.2e-47 < C < 1.74999999999999992e-7

   1. Initial program 62.2%

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

   3. Taylor expanded in B around -inf 60.2%

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

      1. neg-mul-1 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in C around 0 58.9%

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

   if 2.1999999999999999e-229 < C < 1.2e-47

   1. Initial program 53.5%

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

   3. Taylor expanded in A around -inf 45.0%

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

      1. associate-*r/ 45.0%

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

   5. Simplified 45.0%

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

   if 1.74999999999999992e-7 < C

   1. Initial program 21.2%

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

   3. Taylor expanded in C around inf 67.2%

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

   4. Taylor expanded in A around inf 67.2%

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

Alternative 14: 56.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.05 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{-229}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- B A) B)) PI))))
   (if (<= C -1.05e-72)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (if (<= C 2.4e-229)
       t_0
       (if (<= C 1.45e-47)
         (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
         (if (<= C 6.2e-8) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	double tmp;
	if (C <= -1.05e-72) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (C <= 2.4e-229) {
		tmp = t_0;
	} else if (C <= 1.45e-47) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (C <= 6.2e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	double tmp;
	if (C <= -1.05e-72) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (C <= 2.4e-229) {
		tmp = t_0;
	} else if (C <= 1.45e-47) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (C <= 6.2e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	tmp = 0
	if C <= -1.05e-72:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif C <= 2.4e-229:
		tmp = t_0
	elif C <= 1.45e-47:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif C <= 6.2e-8:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi))
	tmp = 0.0
	if (C <= -1.05e-72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (C <= 2.4e-229)
		tmp = t_0;
	elseif (C <= 1.45e-47)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (C <= 6.2e-8)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B - A) / B)) / pi);
	tmp = 0.0;
	if (C <= -1.05e-72)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (C <= 2.4e-229)
		tmp = t_0;
	elseif (C <= 1.45e-47)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (C <= 6.2e-8)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.05e-72], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.4e-229], t$95$0, If[LessEqual[C, 1.45e-47], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.2e-8], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.05e-72

   1. Initial program 68.6%

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

   3. Taylor expanded in B around -inf 66.9%

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

      1. neg-mul-1 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in A around 0 64.5%

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

   if -1.05e-72 < C < 2.4e-229 or 1.45e-47 < C < 6.2e-8

   1. Initial program 64.1%

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

   3. Taylor expanded in B around -inf 59.4%

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

      1. neg-mul-1 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in C around 0 58.2%

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

   if 2.4e-229 < C < 1.45e-47

   1. Initial program 53.5%

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

   3. Taylor expanded in A around -inf 45.0%

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

      1. associate-*r/ 45.0%

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

   5. Simplified 45.0%

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

   if 6.2e-8 < C

   1. Initial program 21.2%

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

   3. Taylor expanded in C around inf 67.2%

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

   4. Taylor expanded in A around inf 67.2%

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

Alternative 15: 66.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 8.6 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 8.6e-244)
   (* 180.0 (/ (atan (* (/ 1.0 B) (+ B (- C A)))) PI))
   (if (<= B 2.55e-231)
     (/ (* 180.0 (atan 0.0)) PI)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.6e-244) {
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / ((double) M_PI));
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.6e-244) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (B + (C - A)))) / Math.PI);
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 8.6e-244:
		tmp = 180.0 * (math.atan(((1.0 / B) * (B + (C - A)))) / math.pi)
	elif B <= 2.55e-231:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 8.6e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B + Float64(C - A)))) / pi));
	elseif (B <= 2.55e-231)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 8.6e-244)
		tmp = 180.0 * (atan(((1.0 / B) * (B + (C - A)))) / pi);
	elseif (B <= 2.55e-231)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 8.6e-244], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B + N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.55e-231], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 8.59999999999999973e-244

   1. Initial program 56.0%

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

   3. Taylor expanded in B around -inf 65.9%

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

      1. neg-mul-1 65.9%

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

   5. Simplified 65.9%

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

   if 8.59999999999999973e-244 < B < 2.55e-231

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 2.55e-231 < B

   1. Initial program 52.7%

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

   3. Taylor expanded in B around inf 69.2%

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

   4. Taylor expanded in B around 0 69.2%

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

      1. associate--r+ 69.2%

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

      2. sub-neg 69.2%

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

      3. mul-1-neg 69.2%

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

      4. mul-1-neg 69.2%

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

      5. sub-neg 69.2%

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

      6. div-sub 69.3%

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

      7. sub-neg 69.3%

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

      8. *-inverses 69.3%

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

      9. metadata-eval 69.3%

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

   6. Simplified 69.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 8.6 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 7.8e-244)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 2.55e-231)
       (/ (* 180.0 (atan 0.0)) PI)
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 7.8e-244) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 7.8e-244) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 2.55e-231) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 7.8e-244:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 2.55e-231:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 7.8e-244)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 2.55e-231)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 7.8e-244)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 2.55e-231)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 7.8e-244], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.55e-231], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 7.7999999999999998e-244

   1. Initial program 56.0%

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

      1. associate-*r/ 56.0%

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

      2. associate-*l/ 56.0%

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

      3. *-un-lft-identity 56.0%

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

      4. unpow2 56.0%

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

      5. unpow2 56.0%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around -inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. div-sub 65.9%

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

   7. Simplified 65.9%

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

   if 7.7999999999999998e-244 < B < 2.55e-231

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 2.55e-231 < B

   1. Initial program 52.7%

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

   3. Taylor expanded in B around inf 69.2%

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

   4. Taylor expanded in B around 0 69.2%

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

      1. associate--r+ 69.2%

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

      2. sub-neg 69.2%

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

      3. mul-1-neg 69.2%

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

      4. mul-1-neg 69.2%

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

      5. sub-neg 69.2%

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

      6. div-sub 69.3%

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

      7. sub-neg 69.3%

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

      8. *-inverses 69.3%

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

      9. metadata-eval 69.3%

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

   6. Simplified 69.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-231}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 7.8e-244)
     (* 180.0 (/ (atan (+ t_0 1.0)) PI))
     (if (<= B 5e-230)
       (/ (* 180.0 (atan 0.0)) PI)
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 7.8e-244) {
		tmp = 180.0 * (atan((t_0 + 1.0)) / ((double) M_PI));
	} else if (B <= 5e-230) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 7.8e-244) {
		tmp = 180.0 * (Math.atan((t_0 + 1.0)) / Math.PI);
	} else if (B <= 5e-230) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 7.8e-244:
		tmp = 180.0 * (math.atan((t_0 + 1.0)) / math.pi)
	elif B <= 5e-230:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 7.8e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + 1.0)) / pi));
	elseif (B <= 5e-230)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 7.8e-244)
		tmp = 180.0 * (atan((t_0 + 1.0)) / pi);
	elseif (B <= 5e-230)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 7.8e-244], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-230], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 7.7999999999999998e-244

   1. Initial program 56.0%

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

   3. Taylor expanded in B around -inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. div-sub 65.9%

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

   5. Simplified 65.9%

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

   if 7.7999999999999998e-244 < B < 5.00000000000000035e-230

   1. Initial program 41.9%

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

      1. associate-*r/ 41.9%

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

      2. associate-*l/ 41.9%

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

      3. *-un-lft-identity 41.9%

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

      4. unpow2 41.9%

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

      5. unpow2 41.9%

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

      6. hypot-define 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. div-sub 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in C around inf 60.0%

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

      1. distribute-lft1-in 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r* 60.0%

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

      4. metadata-eval 60.0%

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

      5. mul0-lft 100.0%

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

   9. Simplified 100.0%

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

   if 5.00000000000000035e-230 < B

   1. Initial program 52.7%

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

   3. Taylor expanded in B around inf 69.2%

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

   4. Taylor expanded in B around 0 69.2%

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

      1. associate--r+ 69.2%

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

      2. sub-neg 69.2%

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

      3. mul-1-neg 69.2%

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

      4. mul-1-neg 69.2%

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

      5. sub-neg 69.2%

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

      6. div-sub 69.3%

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

      7. sub-neg 69.3%

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

      8. *-inverses 69.3%

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

      9. metadata-eval 69.3%

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

   6. Simplified 69.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-74}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.75e-188)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.5e-268)
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
     (if (<= B 2.55e-74)
       (/ (* 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 <= -2.75e-188) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.5e-268) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.55e-74) {
		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 <= -2.75e-188) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.5e-268) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.55e-74) {
		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 <= -2.75e-188:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.5e-268:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.55e-74:
		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 <= -2.75e-188)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.5e-268)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.55e-74)
		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 <= -2.75e-188)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.5e-268)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.55e-74)
		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, -2.75e-188], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-268], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.55e-74], 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 4 regimes

2. if B < -2.7500000000000001e-188

   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. Taylor expanded in B around -inf 48.5%

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

   if -2.7500000000000001e-188 < B < 2.5e-268

   1. Initial program 70.6%

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

   3. Taylor expanded in A around inf 54.8%

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

   if 2.5e-268 < B < 2.5499999999999998e-74

   1. Initial program 45.3%

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

      1. associate-*r/ 45.3%

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

      2. associate-*l/ 45.2%

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

      3. *-un-lft-identity 45.2%

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

      4. unpow2 45.2%

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

      5. unpow2 45.2%

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

      6. hypot-define 77.0%

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

   4. Applied egg-rr 77.0%

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

      1. div-sub 39.2%

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

   6. Applied egg-rr 39.2%

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

   7. Taylor expanded in C around inf 15.8%

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

      1. distribute-lft1-in 15.8%

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

      2. metadata-eval 15.8%

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

      3. associate-*r* 15.8%

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

      4. metadata-eval 15.8%

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

      5. mul0-lft 40.4%

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

   9. Simplified 40.4%

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

   if 2.5499999999999998e-74 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 58.2%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-74}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.75e-188)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.4e-279)
     (* 180.0 (/ (atan (/ A (- B))) PI))
     (if (<= B 3.6e-75)
       (/ (* 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 <= -2.75e-188) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.4e-279) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 3.6e-75) {
		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 <= -2.75e-188) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.4e-279) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 3.6e-75) {
		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 <= -2.75e-188:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.4e-279:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 3.6e-75:
		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 <= -2.75e-188)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.4e-279)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 3.6e-75)
		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 <= -2.75e-188)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.4e-279)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 3.6e-75)
		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, -2.75e-188], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-279], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-75], 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 4 regimes

2. if B < -2.7500000000000001e-188

   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. Taylor expanded in B around -inf 48.5%

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

   if -2.7500000000000001e-188 < B < 2.3999999999999999e-279

   1. Initial program 71.9%

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

   3. Taylor expanded in B around inf 59.3%

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

   4. Taylor expanded in A around inf 54.9%

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

      1. associate-*r/ 54.9%

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

      2. mul-1-neg 54.9%

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

   6. Simplified 54.9%

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

   if 2.3999999999999999e-279 < B < 3.6e-75

   1. Initial program 45.6%

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

      1. associate-*r/ 45.6%

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

      2. associate-*l/ 45.6%

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

      3. *-un-lft-identity 45.6%

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

      4. unpow2 45.6%

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

      5. unpow2 45.6%

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

      6. hypot-define 78.2%

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

   4. Applied egg-rr 78.2%

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

      1. div-sub 39.7%

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

   6. Applied egg-rr 39.7%

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

   7. Taylor expanded in C around inf 15.0%

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

      1. distribute-lft1-in 15.0%

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

      2. metadata-eval 15.0%

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

      3. associate-*r* 15.0%

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

      4. metadata-eval 15.0%

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

      5. mul0-lft 40.9%

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

   9. Simplified 40.9%

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

   if 3.6e-75 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 58.2%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.05e-78)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7.2e-280)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 5.2e-75)
       (/ (* 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 <= -2.05e-78) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.2e-280) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 5.2e-75) {
		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 <= -2.05e-78) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.2e-280) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 5.2e-75) {
		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 <= -2.05e-78:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.2e-280:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 5.2e-75:
		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 <= -2.05e-78)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.2e-280)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 5.2e-75)
		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 <= -2.05e-78)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.2e-280)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 5.2e-75)
		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, -2.05e-78], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-280], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.2e-75], 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 4 regimes

2. if B < -2.0499999999999999e-78

   1. Initial program 46.4%

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

   3. Taylor expanded in B around -inf 55.1%

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

   if -2.0499999999999999e-78 < B < 7.19999999999999989e-280

   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 54.9%

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

   4. Taylor expanded in C around inf 39.2%

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

   if 7.19999999999999989e-280 < B < 5.2e-75

   1. Initial program 45.6%

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

      1. associate-*r/ 45.6%

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

      2. associate-*l/ 45.6%

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

      3. *-un-lft-identity 45.6%

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

      4. unpow2 45.6%

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

      5. unpow2 45.6%

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

      6. hypot-define 78.2%

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

   4. Applied egg-rr 78.2%

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

      1. div-sub 39.7%

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

   6. Applied egg-rr 39.7%

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

   7. Taylor expanded in C around inf 15.0%

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

      1. distribute-lft1-in 15.0%

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

      2. metadata-eval 15.0%

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

      3. associate-*r* 15.0%

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

      4. metadata-eval 15.0%

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

      5. mul0-lft 40.9%

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

   9. Simplified 40.9%

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

   if 5.2e-75 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 58.2%

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

Alternative 21: 45.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.46 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.46e-173)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e-75)
     (/ (* 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 <= -1.46e-173) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-75) {
		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 <= -1.46e-173) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-75) {
		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 <= -1.46e-173:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-75:
		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 <= -1.46e-173)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-75)
		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 <= -1.46e-173)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-75)
		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, -1.46e-173], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-75], 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 < -1.46e-173

   1. Initial program 52.5%

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

   3. Taylor expanded in B around -inf 50.0%

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

   if -1.46e-173 < B < 4.80000000000000039e-75

   1. Initial program 55.0%

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

      1. associate-*r/ 55.0%

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

      2. associate-*l/ 55.0%

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

      3. *-un-lft-identity 55.0%

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

      4. unpow2 55.0%

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

      5. unpow2 55.0%

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

      6. hypot-define 79.1%

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

   4. Applied egg-rr 79.1%

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

      1. div-sub 46.5%

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

   6. Applied egg-rr 46.5%

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

   7. Taylor expanded in C around inf 11.7%

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

      1. distribute-lft1-in 11.7%

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

      2. metadata-eval 11.7%

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

      3. associate-*r* 11.7%

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

      4. metadata-eval 11.7%

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

      5. mul0-lft 35.3%

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

   9. Simplified 35.3%

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

   if 4.80000000000000039e-75 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 58.2%

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

Alternative 22: 40.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-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 <= -4e-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 <= -4e-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 <= -4e-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 <= -4e-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 <= -4e-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, -4e-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 < -3.999999999999988e-310

   1. Initial program 54.3%

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

   3. Taylor expanded in B around -inf 41.1%

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

   if -3.999999999999988e-310 < B

   1. Initial program 54.1%

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

   3. Taylor expanded in B around inf 42.3%

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

Alternative 23: 21.9% 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 54.2%

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

3. Taylor expanded in B around inf 23.5%

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

Reproduce

herbie shell --seed 2024110 
(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)))