ABCF->ab-angle angle

Percentage Accurate: 53.7% → 81.5%

Time: 16.3s

Alternatives: 19

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (/ 1.0 (/ PI (* 180.0 (atan (/ (- (- C A) (hypot B (- A C))) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else {
		tmp = 1.0 / (((double) M_PI) / (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else {
		tmp = 1.0 / (Math.PI / (180.0 * Math.atan((((C - A) - Math.hypot(B, (A - C))) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	else:
		tmp = 1.0 / (math.pi / (180.0 * math.atan((((C - A) - math.hypot(B, (A - C))) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(1.0 / Float64(pi / Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	else
		tmp = 1.0 / (pi / (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(Pi / N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.7000000000000002e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -2.7000000000000002e143 < A

   1. Initial program 63.6%

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

      1. associate-*r/ 63.6%

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

   4. Applied egg-rr 84.0%

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

Alternative 2: 77.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-134}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\pi}{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.6e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (if (<= A 1.3e-134)
     (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
     (/ 1.0 (/ PI (* -180.0 (atan (/ (+ A (hypot B A)) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.6e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else if (A <= 1.3e-134) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else {
		tmp = 1.0 / (((double) M_PI) / (-180.0 * atan(((A + hypot(B, A)) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.6e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else if (A <= 1.3e-134) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else {
		tmp = 1.0 / (Math.PI / (-180.0 * Math.atan(((A + Math.hypot(B, A)) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.6e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	elif A <= 1.3e-134:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	else:
		tmp = 1.0 / (math.pi / (-180.0 * math.atan(((A + math.hypot(B, A)) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.6e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 1.3e-134)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	else
		tmp = Float64(1.0 / Float64(pi / Float64(-180.0 * atan(Float64(Float64(A + hypot(B, A)) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.6e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	elseif (A <= 1.3e-134)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	else
		tmp = 1.0 / (pi / (-180.0 * atan(((A + hypot(B, A)) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.6e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.3e-134], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(1.0 / N[(Pi / N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.60000000000000008e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -1.60000000000000008e143 < A < 1.30000000000000011e-134

   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. Step-by-step derivation

      1. associate-*r/ 56.8%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in A around 0 54.5%

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

      1. +-commutative 54.5%

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

      2. unpow2 54.5%

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

      3. unpow2 54.5%

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

      4. hypot-define 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in C around 0 54.5%

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

      1. +-commutative 54.5%

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

      2. unpow2 54.5%

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

      3. unpow2 54.5%

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

      4. hypot-undefine 74.5%

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

      5. associate-/l* 74.5%

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

   10. Simplified 74.5%

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

   if 1.30000000000000011e-134 < A

   1. Initial program 72.5%

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

      1. associate-*r/ 72.5%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in C around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. distribute-neg-frac2 70.9%

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

      3. unpow2 70.9%

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

      4. unpow2 70.9%

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

      5. hypot-define 88.6%

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

   7. Simplified 88.6%

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

      1. inv-pow 88.6%

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

      2. associate-/r* 88.6%

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

      3. distribute-frac-neg2 88.6%

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

      4. atan-neg 88.6%

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

   9. Applied egg-rr 88.6%

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

       1. unpow-1 88.6%

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

       2. associate-/l/ 88.6%

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

       3. *-commutative 88.6%

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

       4. distribute-rgt-neg-out 88.6%

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

       5. distribute-lft-neg-in 88.6%

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

       6. metadata-eval 88.6%

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

       7. hypot-undefine 70.9%

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

       8. unpow2 70.9%

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

       9. unpow2 70.9%

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

       10. +-commutative 70.9%

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

       11. unpow2 70.9%

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

       12. unpow2 70.9%

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

       13. hypot-define 88.6%

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

   11. Simplified 88.6%

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

Alternative 3: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.7e+144)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- A C) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.7e+144) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((A - C), B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.7e+144) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((A - C), B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.7e+144:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((A - C), B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.7e+144)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(A - C), B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.7e+144)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((A - C), B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.7e+144], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.6999999999999997e144

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -3.6999999999999997e144 < A

   1. Initial program 63.6%

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

      1. unpow2 63.6%

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

      2. unpow2 63.6%

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

      3. hypot-define 84.0%

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

   4. Applied egg-rr 84.0%

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

Alternative 4: 77.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-134}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.4e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (if (<= A 1.45e-134)
     (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
     (/ (* -180.0 (atan (/ (+ A (hypot B A)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else if (A <= 1.45e-134) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / 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 <= -5.4e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else if (A <= 1.45e-134) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / 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 <= -5.4e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	elif A <= 1.45e-134:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / 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 <= -5.4e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 1.45e-134)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(B, A)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.4e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	elseif (A <= 1.45e-134)
		tmp = (180.0 * atan(((C - hypot(C, B)) / 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, -5.4e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.45e-134], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.4000000000000003e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -5.4000000000000003e143 < A < 1.44999999999999997e-134

   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. Step-by-step derivation

      1. associate-*r/ 56.8%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in A around 0 54.5%

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

      1. +-commutative 54.5%

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

      2. unpow2 54.5%

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

      3. unpow2 54.5%

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

      4. hypot-define 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in C around 0 54.5%

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

      1. +-commutative 54.5%

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

      2. unpow2 54.5%

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

      3. unpow2 54.5%

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

      4. hypot-undefine 74.5%

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

      5. associate-/l* 74.5%

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

   10. Simplified 74.5%

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

   if 1.44999999999999997e-134 < A

   1. Initial program 72.5%

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

      1. associate-*r/ 72.5%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in C around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. distribute-neg-frac2 70.9%

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

      3. unpow2 70.9%

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

      4. unpow2 70.9%

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

      5. hypot-define 88.6%

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

   7. Simplified 88.6%

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

      1. *-un-lft-identity 88.6%

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

      2. associate-/r/ 88.6%

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

      3. distribute-frac-neg2 88.6%

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

      4. atan-neg 88.6%

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

   9. Applied egg-rr 88.6%

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

       1. *-lft-identity 88.6%

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

       2. associate-*l/ 88.6%

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

       3. *-lft-identity 88.6%

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

       4. distribute-rgt-neg-out 88.6%

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

       5. distribute-lft-neg-in 88.6%

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

       6. metadata-eval 88.6%

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

       7. hypot-undefine 70.9%

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

       8. unpow2 70.9%

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

       9. unpow2 70.9%

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

       10. +-commutative 70.9%

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

       11. unpow2 70.9%

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

       12. unpow2 70.9%

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

       13. hypot-define 88.6%

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

   11. Simplified 88.6%

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

Alternative 5: 77.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.45 \cdot 10^{+149}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.06 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.45e+149)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (if (<= A 1.06e-134)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ (* -180.0 (atan (/ (+ A (hypot B A)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.45e+149) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else if (A <= 1.06e-134) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / 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 <= -3.45e+149) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else if (A <= 1.06e-134) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / 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 <= -3.45e+149:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	elif A <= 1.06e-134:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / 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 <= -3.45e+149)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 1.06e-134)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(B, A)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.45e+149)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	elseif (A <= 1.06e-134)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / 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, -3.45e+149], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.06e-134], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.4500000000000002e149

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -3.4500000000000002e149 < A < 1.06e-134

   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 A around 0 54.5%

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

      1. +-commutative 54.5%

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

      2. unpow2 54.5%

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

      3. unpow2 54.5%

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

      4. hypot-define 74.5%

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

   5. Simplified 74.5%

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

   if 1.06e-134 < A

   1. Initial program 72.5%

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

      1. associate-*r/ 72.5%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in C around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. distribute-neg-frac2 70.9%

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

      3. unpow2 70.9%

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

      4. unpow2 70.9%

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

      5. hypot-define 88.6%

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

   7. Simplified 88.6%

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

      1. *-un-lft-identity 88.6%

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

      2. associate-/r/ 88.6%

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

      3. distribute-frac-neg2 88.6%

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

      4. atan-neg 88.6%

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

   9. Applied egg-rr 88.6%

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

       1. *-lft-identity 88.6%

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

       2. associate-*l/ 88.6%

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

       3. *-lft-identity 88.6%

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

       4. distribute-rgt-neg-out 88.6%

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

       5. distribute-lft-neg-in 88.6%

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

       6. metadata-eval 88.6%

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

       7. hypot-undefine 70.9%

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

       8. unpow2 70.9%

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

       9. unpow2 70.9%

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

       10. +-commutative 70.9%

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

       11. unpow2 70.9%

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

       12. unpow2 70.9%

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

       13. hypot-define 88.6%

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

   11. Simplified 88.6%

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

Alternative 6: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.4e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (if (<= A 4.8e+22)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ 180.0 (/ PI (atan (+ (/ (- C A) B) -1.0)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else if (A <= 4.8e+22) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) / B) + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else if (A <= 4.8e+22) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) / B) + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.4e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	elif A <= 4.8e+22:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) / B) + -1.0)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.4e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 4.8e+22)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) / B) + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.4e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	elseif (A <= 4.8e+22)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan((((C - A) / B) + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.4e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.8e+22], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.40000000000000033e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -6.40000000000000033e143 < A < 4.8e22

   1. Initial program 59.1%

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

   3. Taylor expanded in A around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. unpow2 54.8%

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

      3. unpow2 54.8%

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

      4. hypot-define 75.6%

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

   5. Simplified 75.6%

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

   if 4.8e22 < A

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate--l- 78.1%

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

      3. +-commutative 78.1%

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

      4. unpow2 78.1%

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

      5. unpow2 78.1%

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

      6. hypot-undefine 96.3%

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

      7. div-inv 96.3%

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

      8. clear-num 96.3%

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

      9. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in B around inf 76.2%

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

      1. +-commutative 76.2%

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

      2. associate--r+ 76.2%

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

      3. div-sub 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (/ (* 180.0 (atan (/ (- (- C A) (hypot B (- A C))) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else {
		tmp = (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot(B, (A - C))) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot(B, (A - C))) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	else
		tmp = (180.0 * atan((((C - A) - hypot(B, (A - C))) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.0000000000000001e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -6.0000000000000001e143 < A

   1. Initial program 63.6%

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

      1. associate-*r/ 63.6%

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

   4. Applied egg-rr 84.0%

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

Alternative 8: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e+149)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e+149) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e+149) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9e+149:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9e+149)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	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 <= -9e+149)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9e+149], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 < -8.99999999999999965e149

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -8.99999999999999965e149 < A

   1. Initial program 63.6%

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

      1. associate-*l/ 63.6%

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

      2. *-lft-identity 63.6%

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

      3. +-commutative 63.6%

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

      4. unpow2 63.6%

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

      5. unpow2 63.6%

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

      6. hypot-define 84.0%

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

   3. Simplified 84.0%

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

Alternative 9: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.52 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.52e+143)
   (* (/ 1.0 PI) (* 180.0 (atan (* 0.5 (/ B A)))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.52e+143) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.52e+143) {
		tmp = (1.0 / Math.PI) * (180.0 * Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.52e+143:
		tmp = (1.0 / math.pi) * (180.0 * math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.52e+143)
		tmp = Float64(Float64(1.0 / pi) * Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.52e+143)
		tmp = (1.0 / pi) * (180.0 * atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.52e+143], N[(N[(1.0 / Pi), $MachinePrecision] * N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.51999999999999996e143

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in A around -inf 85.2%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -1.51999999999999996e143 < A

   1. Initial program 63.6%

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

   3. Simplified 83.3%

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

Alternative 10: 65.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + t\_0\right)}}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + \frac{B \cdot C}{A}\right)}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.6e-188)
     (/ 180.0 (/ PI (atan (+ 1.0 t_0))))
     (if (<= B 4.7e-285)
       (* 180.0 (/ (atan (/ (* -0.5 (+ B (/ (* B C) A))) (- A))) PI))
       (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.6e-188) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + t_0)));
	} else if (B <= 4.7e-285) {
		tmp = 180.0 * (atan(((-0.5 * (B + ((B * C) / A))) / -A)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.6e-188) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + t_0)));
	} else if (B <= 4.7e-285) {
		tmp = 180.0 * (Math.atan(((-0.5 * (B + ((B * C) / A))) / -A)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.6e-188:
		tmp = 180.0 / (math.pi / math.atan((1.0 + t_0)))
	elif B <= 4.7e-285:
		tmp = 180.0 * (math.atan(((-0.5 * (B + ((B * C) / A))) / -A)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.6e-188)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + t_0))));
	elseif (B <= 4.7e-285)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B + Float64(Float64(B * C) / A))) / Float64(-A))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.6e-188)
		tmp = 180.0 / (pi / atan((1.0 + t_0)));
	elseif (B <= 4.7e-285)
		tmp = 180.0 * (atan(((-0.5 * (B + ((B * C) / A))) / -A)) / pi);
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.6e-188], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.7e-285], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B + N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.60000000000000011e-188

   1. Initial program 57.7%

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

      1. *-commutative 57.7%

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

      2. associate--l- 57.6%

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

      3. +-commutative 57.6%

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

      4. unpow2 57.6%

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

      5. unpow2 57.6%

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

      6. hypot-undefine 81.1%

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

      7. div-inv 81.1%

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

      8. clear-num 81.1%

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

      9. un-div-inv 81.1%

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

   4. Applied egg-rr 84.1%

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

   5. Taylor expanded in B around -inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. div-sub 78.1%

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

   7. Simplified 78.1%

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

   if -1.60000000000000011e-188 < B < 4.70000000000000037e-285

   1. Initial program 48.5%

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

   3. Taylor expanded in A around -inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. mul-1-neg 62.9%

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

      3. distribute-lft-out 62.9%

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

      4. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   if 4.70000000000000037e-285 < B

   1. Initial program 55.8%

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

      1. *-commutative 55.8%

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

      2. associate--l- 55.8%

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

      3. +-commutative 55.8%

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

      4. unpow2 55.8%

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

      5. unpow2 55.8%

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

      6. hypot-undefine 73.7%

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

      7. div-inv 73.6%

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

      8. clear-num 73.6%

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

      9. un-div-inv 73.6%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in B around inf 64.3%

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

      1. +-commutative 64.3%

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

      2. associate--r+ 64.3%

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

      3. div-sub 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + \frac{B \cdot C}{A}\right)}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -7.1 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + t\_0\right)}}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -7.1e-189)
     (/ 180.0 (/ PI (atan (+ 1.0 t_0))))
     (if (<= B 2.4e-286)
       (/ 180.0 (/ PI (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))))
       (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -7.1e-189) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + t_0)));
	} else if (B <= 2.4e-286) {
		tmp = 180.0 / (((double) M_PI) / atan(((0.5 * (B + (B * (C / A)))) / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -7.1e-189) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + t_0)));
	} else if (B <= 2.4e-286) {
		tmp = 180.0 / (Math.PI / Math.atan(((0.5 * (B + (B * (C / A)))) / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -7.1e-189:
		tmp = 180.0 / (math.pi / math.atan((1.0 + t_0)))
	elif B <= 2.4e-286:
		tmp = 180.0 / (math.pi / math.atan(((0.5 * (B + (B * (C / A)))) / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -7.1e-189)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + t_0))));
	elseif (B <= 2.4e-286)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -7.1e-189)
		tmp = 180.0 / (pi / atan((1.0 + t_0)));
	elseif (B <= 2.4e-286)
		tmp = 180.0 / (pi / atan(((0.5 * (B + (B * (C / A)))) / A)));
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -7.1e-189], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-286], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.1000000000000003e-189

   1. Initial program 57.7%

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

      1. *-commutative 57.7%

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

      2. associate--l- 57.6%

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

      3. +-commutative 57.6%

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

      4. unpow2 57.6%

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

      5. unpow2 57.6%

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

      6. hypot-undefine 81.1%

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

      7. div-inv 81.1%

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

      8. clear-num 81.1%

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

      9. un-div-inv 81.1%

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

   4. Applied egg-rr 84.1%

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

   5. Taylor expanded in B around -inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. div-sub 78.1%

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

   7. Simplified 78.1%

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

   if -7.1000000000000003e-189 < B < 2.39999999999999993e-286

   1. Initial program 48.3%

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

      1. *-commutative 48.3%

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

      2. associate--l- 43.3%

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

      3. +-commutative 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-undefine 50.0%

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

      7. div-inv 50.0%

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

      8. clear-num 50.0%

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

      9. un-div-inv 50.0%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in A around -inf 62.3%

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

      1. associate-*r/ 62.3%

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

      2. distribute-lft-out 62.3%

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

      3. associate-*r* 62.3%

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

      4. metadata-eval 62.3%

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

      5. associate-/l* 61.9%

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

   7. Simplified 61.9%

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

   if 2.39999999999999993e-286 < B

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. associate--l- 55.7%

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

      3. +-commutative 55.7%

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

      4. unpow2 55.7%

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

      5. unpow2 55.7%

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

      6. hypot-undefine 73.3%

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

      7. div-inv 73.3%

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

      8. clear-num 73.3%

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

      9. un-div-inv 73.3%

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

   4. Applied egg-rr 79.2%

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

   5. Taylor expanded in B around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. associate--r+ 63.3%

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

      3. div-sub 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.1 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-286}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.32 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.32e-45)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -6.5e-193)
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
     (if (<= B 4.3e-75)
       (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.32e-45) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6.5e-193) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 4.3e-75) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((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 <= -1.32e-45) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6.5e-193) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 4.3e-75) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.32e-45:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6.5e-193:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 4.3e-75:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / 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 <= -1.32e-45)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6.5e-193)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 4.3e-75)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / 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 <= -1.32e-45)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6.5e-193)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 4.3e-75)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.32e-45], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.5e-193], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.3e-75], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.32000000000000005e-45

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 69.0%

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

   if -1.32000000000000005e-45 < B < -6.5000000000000004e-193

   1. Initial program 60.4%

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

      1. associate-*l/ 60.4%

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

      2. *-lft-identity 60.4%

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

      3. +-commutative 60.4%

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

      4. unpow2 60.4%

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

      5. unpow2 60.4%

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

      6. hypot-define 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in A around inf 46.1%

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

      1. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   if -6.5000000000000004e-193 < B < 4.2999999999999999e-75

   1. Initial program 57.6%

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

   3. Taylor expanded in A around -inf 42.2%

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

      1. associate-*r/ 42.2%

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

   5. Simplified 42.2%

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

   if 4.2999999999999999e-75 < B

   1. Initial program 50.6%

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

   3. Taylor expanded in B around inf 67.1%

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

Alternative 13: 64.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -5.8 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + t\_0\right)}}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -5.8e-189)
     (/ 180.0 (/ PI (atan (+ 1.0 t_0))))
     (if (<= B 4e-295)
       (/ 180.0 (/ PI (atan 0.0)))
       (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.8e-189) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + t_0)));
	} else if (B <= 4e-295) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.8e-189) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + t_0)));
	} else if (B <= 4e-295) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -5.8e-189:
		tmp = 180.0 / (math.pi / math.atan((1.0 + t_0)))
	elif B <= 4e-295:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -5.8e-189)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + t_0))));
	elseif (B <= 4e-295)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -5.8e-189)
		tmp = 180.0 / (pi / atan((1.0 + t_0)));
	elseif (B <= 4e-295)
		tmp = 180.0 / (pi / atan(0.0));
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -5.8e-189], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-295], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.8e-189

   1. Initial program 57.7%

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

      1. *-commutative 57.7%

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

      2. associate--l- 57.6%

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

      3. +-commutative 57.6%

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

      4. unpow2 57.6%

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

      5. unpow2 57.6%

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

      6. hypot-undefine 81.1%

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

      7. div-inv 81.1%

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

      8. clear-num 81.1%

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

      9. un-div-inv 81.1%

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

   4. Applied egg-rr 84.1%

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

   5. Taylor expanded in B around -inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. div-sub 78.1%

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

   7. Simplified 78.1%

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

   if -5.8e-189 < B < 4.00000000000000024e-295

   1. Initial program 48.1%

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

      1. *-commutative 48.1%

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

      2. associate--l- 42.7%

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

      3. +-commutative 42.7%

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

      4. unpow2 42.7%

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

      5. unpow2 42.7%

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

      6. hypot-undefine 49.9%

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

      7. div-inv 49.9%

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

      8. clear-num 49.9%

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

      9. un-div-inv 49.9%

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

   4. Applied egg-rr 87.6%

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

      1. div-sub 33.9%

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

   6. Applied egg-rr 33.9%

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

   7. Taylor expanded in C around inf 16.1%

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

      1. distribute-lft1-in 16.1%

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

      2. metadata-eval 16.1%

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

      3. associate-*r* 16.1%

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

      4. metadata-eval 16.1%

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

      5. mul0-lft 55.3%

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

   9. Simplified 55.3%

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

   if 4.00000000000000024e-295 < B

   1. Initial program 55.6%

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

      1. *-commutative 55.6%

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

      2. associate--l- 55.7%

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

      3. +-commutative 55.7%

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

      4. unpow2 55.7%

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

      5. unpow2 55.7%

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

      6. hypot-undefine 73.0%

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

      7. div-inv 72.9%

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

      8. clear-num 72.9%

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

      9. un-div-inv 72.9%

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

   4. Applied egg-rr 78.8%

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

   5. Taylor expanded in B around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. associate--r+ 63.1%

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

      3. div-sub 67.1%

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

   7. Simplified 67.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.22 \cdot 10^{-108}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.22e-108)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.35e-75)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.22e-108) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.35e-75) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((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 <= -1.22e-108) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.35e-75) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.22e-108:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.35e-75:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / 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 <= -1.22e-108)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.35e-75)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / 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 <= -1.22e-108)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.35e-75)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.22e-108], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-75], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.2199999999999999e-108

   1. Initial program 58.1%

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

   3. Taylor expanded in B around -inf 60.2%

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

   if -1.2199999999999999e-108 < B < 1.3499999999999999e-75

   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 A around -inf 40.8%

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

      1. associate-*r/ 40.8%

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

   5. Simplified 40.8%

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

   if 1.3499999999999999e-75 < B

   1. Initial program 50.6%

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

   3. Taylor expanded in B around inf 67.1%

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

Alternative 15: 59.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.4 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.4e-58)
   (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B)))))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-58) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-58) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.4e-58:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.4e-58)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.4e-58)
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.4e-58], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 5.3999999999999998e-58

   1. Initial program 57.6%

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

      1. *-commutative 57.6%

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

      2. associate--l- 56.8%

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

      3. +-commutative 56.8%

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

      4. unpow2 56.8%

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

      5. unpow2 56.8%

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

      6. hypot-undefine 72.5%

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

      7. div-inv 72.5%

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

      8. clear-num 72.4%

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

      9. un-div-inv 72.4%

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in B around -inf 61.0%

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

      1. associate--l+ 61.0%

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

      2. div-sub 64.7%

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

   7. Simplified 64.7%

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

   if 5.3999999999999998e-58 < B

   1. Initial program 49.8%

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

   3. Taylor expanded in B around inf 67.8%

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

Alternative 16: 59.9% accurate, 3.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if B < 6.00000000000000015e-58

   1. Initial program 57.6%

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

   3. Taylor expanded in B around -inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. div-sub 64.7%

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

   5. Simplified 64.7%

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

   if 6.00000000000000015e-58 < B

   1. Initial program 49.8%

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

   3. Taylor expanded in B around inf 67.8%

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

Alternative 17: 45.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.7e-110)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.35e-99)
     (/ 180.0 (/ PI (atan 0.0)))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-110) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.35e-99) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-110) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.35e-99) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.7e-110:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.35e-99:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.7e-110)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.35e-99)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	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 <= -2.7e-110)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.35e-99)
		tmp = 180.0 / (pi / atan(0.0));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.7e-110], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-99], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.6999999999999998e-110

   1. Initial program 58.1%

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

   3. Taylor expanded in B around -inf 60.2%

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

   if -2.6999999999999998e-110 < B < 1.35e-99

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. associate--l- 54.2%

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

      3. +-commutative 54.2%

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

      4. unpow2 54.2%

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

      5. unpow2 54.2%

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

      6. hypot-undefine 60.8%

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

      7. div-inv 60.8%

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

      8. clear-num 60.8%

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

      9. un-div-inv 60.8%

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

   4. Applied egg-rr 81.5%

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

      1. div-sub 51.1%

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

   6. Applied egg-rr 51.1%

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

   7. Taylor expanded in C around inf 9.1%

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

      1. distribute-lft1-in 9.1%

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

      2. metadata-eval 9.1%

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

      3. associate-*r* 9.1%

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

      4. metadata-eval 9.1%

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

      5. mul0-lft 32.9%

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

   9. Simplified 32.9%

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

   if 1.35e-99 < 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 62.0%

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

Alternative 18: 40.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-309) (* 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 <= -1e-309) {
		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 <= -1e-309) {
		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 <= -1e-309:
		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 <= -1e-309)
		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 <= -1e-309)
		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, -1e-309], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.000000000000002e-309

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 44.5%

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

   if -1.000000000000002e-309 < B

   1. Initial program 55.2%

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

   3. Taylor expanded in B around inf 39.9%

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

Alternative 19: 21.2% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.6%

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

3. Taylor expanded in B around inf 21.5%

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

Reproduce

herbie shell --seed 2024188 
(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)))