ABCF->ab-angle angle

Percentage Accurate: 53.5% → 88.4%

Time: 18.0s

Alternatives: 17

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.5% 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: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-41} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -4e-41) (not (<= t_0 0.0)))
     (* (/ 180.0 PI) (atan (/ 1.0 (/ B (- (- C A) (hypot B (- C A)))))))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -4e-41) || !(t_0 <= 0.0)) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 / (B / ((C - A) - hypot(B, (C - A))))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -4e-41) || !(t_0 <= 0.0)) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 / (B / ((C - A) - Math.hypot(B, (C - A))))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -4e-41) or not (t_0 <= 0.0):
		tmp = (180.0 / math.pi) * math.atan((1.0 / (B / ((C - A) - math.hypot(B, (C - A))))))
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -4e-41) || !(t_0 <= 0.0))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 / Float64(B / Float64(Float64(C - A) - hypot(B, Float64(C - A)))))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -4e-41) || ~((t_0 <= 0.0)))
		tmp = (180.0 / pi) * atan((1.0 / (B / ((C - A) - hypot(B, (C - A))))));
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[t$95$0, -4e-41], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 / N[(B / N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.00000000000000002e-41 or -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 61.9%

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

   3. Simplified 82.3%

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

      1. clear-num 82.3%

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

      2. inv-pow 82.3%

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

   5. Applied egg-rr 82.3%

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

      1. unpow-1 82.3%

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

      2. associate--r+ 86.3%

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

   7. Simplified 86.3%

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

   if -4.00000000000000002e-41 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

   1. Initial program 27.2%

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

   3. Simplified 19.5%

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

   4. Taylor expanded in B around 0 99.1%

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

      1. associate-*r/ 99.2%

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

   6. Simplified 99.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -4 \cdot 10^{-41} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \end{array} \]

Alternative 2: 81.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+30)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+30:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+30)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.7999999999999999e30

   1. Initial program 20.2%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in B around 0 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -8.7999999999999999e30 < A

   1. Initial program 67.7%

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

   3. Simplified 86.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 81.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+30)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+30:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+30)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.7999999999999999e30

   1. Initial program 20.2%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in B around 0 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -8.7999999999999999e30 < A

   1. Initial program 67.7%

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

   3. Simplified 86.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 4: 76.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+30)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A 4.5e-7)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= 4.5e-7) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= 4.5e-7) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+30:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= 4.5e-7:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= 4.5e-7)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+30)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= 4.5e-7)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.5e-7], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.7999999999999999e30

   1. Initial program 20.2%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in B around 0 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -8.7999999999999999e30 < A < 4.4999999999999998e-7

   1. Initial program 66.1%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in A around 0 64.1%

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

      1. unpow2 64.1%

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

      2. unpow2 64.1%

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

      3. hypot-def 81.9%

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

   6. Simplified 81.9%

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

   if 4.4999999999999998e-7 < A

   1. Initial program 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in B around -inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. div-sub 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 76.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+30)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A 6.5e-8)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= 6.5e-8) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= 6.5e-8) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+30:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= 6.5e-8:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= 6.5e-8)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+30)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= 6.5e-8)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.5e-8], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.7999999999999999e30

   1. Initial program 20.2%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in B around 0 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -8.7999999999999999e30 < A < 6.49999999999999997e-8

   1. Initial program 66.1%

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

   3. Simplified 84.1%

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

      1. clear-num 84.1%

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

      2. inv-pow 84.1%

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

   5. Applied egg-rr 84.1%

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

      1. unpow-1 84.1%

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

      2. associate--r+ 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in A around 0 64.2%

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

      1. unpow2 64.2%

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

      2. unpow2 64.2%

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

      3. hypot-def 81.9%

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

   10. Simplified 81.9%

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

   if 6.49999999999999997e-8 < A

   1. Initial program 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in B around -inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. div-sub 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 57.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.18 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-289} \lor \neg \left(B \leq 7.2 \cdot 10^{+81}\right) \land B \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.18e-107)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (or (<= B 1.75e-289) (and (not (<= B 7.2e+81)) (<= B 6.2e+104)))
     (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
     (/ (* 180.0 (atan (/ (- C B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.18e-107) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if ((B <= 1.75e-289) || (!(B <= 7.2e+81) && (B <= 6.2e+104))) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.18e-107) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if ((B <= 1.75e-289) || (!(B <= 7.2e+81) && (B <= 6.2e+104))) {
		tmp = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.18e-107:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif (B <= 1.75e-289) or (not (B <= 7.2e+81) and (B <= 6.2e+104)):
		tmp = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.18e-107)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif ((B <= 1.75e-289) || (!(B <= 7.2e+81) && (B <= 6.2e+104)))
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.18e-107)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif ((B <= 1.75e-289) || (~((B <= 7.2e+81)) && (B <= 6.2e+104)))
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	else
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.18e-107], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.75e-289], And[N[Not[LessEqual[B, 7.2e+81]], $MachinePrecision], LessEqual[B, 6.2e+104]]], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.17999999999999993e-107

   1. Initial program 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in B around -inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. div-sub 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in C around inf 79.9%

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

   if -1.17999999999999993e-107 < B < 1.75e-289 or 7.20000000000000011e81 < B < 6.20000000000000033e104

   1. Initial program 52.9%

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

   3. Simplified 57.7%

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

      1. clear-num 57.7%

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

      2. inv-pow 57.7%

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

   5. Applied egg-rr 57.7%

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

      1. unpow-1 57.7%

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

      2. associate--r+ 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in B around 0 55.5%

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

   9. Taylor expanded in C around -inf 56.6%

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

       1. associate-*r/ 56.5%

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

       2. associate-*r/ 56.5%

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

       3. mul-1-neg 56.5%

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

       4. sub-neg 56.5%

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

   11. Simplified 56.5%

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

   12. Taylor expanded in B around 0 56.6%

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

       1. sub-neg 56.6%

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

       2. mul-1-neg 56.6%

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

       3. associate-*r/ 56.6%

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

       4. mul-1-neg 56.6%

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

       5. sub-neg 56.6%

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

       6. *-commutative 56.6%

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

       7. associate-*r/ 56.6%

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

   14. Simplified 56.6%

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

   if 1.75e-289 < B < 7.20000000000000011e81 or 6.20000000000000033e104 < B

   1. Initial program 60.2%

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

      1. associate-*r/ 60.2%

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

      2. associate-*l/ 60.2%

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

      3. *-un-lft-identity 60.2%

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

      4. associate--l- 59.1%

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

      5. unpow2 59.1%

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

      6. pow2 59.1%

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

      7. hypot-def 79.1%

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

   3. Applied egg-rr 79.1%

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

   4. Taylor expanded in B around inf 68.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.18 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-289} \lor \neg \left(B \leq 7.2 \cdot 10^{+81}\right) \land B \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 60.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.55 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-290} \lor \neg \left(B \leq 2.8 \cdot 10^{+81}\right) \land B \leq 9.8 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.55e-256)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (or (<= B 8.6e-290) (and (not (<= B 2.8e+81)) (<= B 9.8e+101)))
     (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
     (/ (* 180.0 (atan (/ (- C B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.55e-256) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if ((B <= 8.6e-290) || (!(B <= 2.8e+81) && (B <= 9.8e+101))) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.55e-256) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if ((B <= 8.6e-290) || (!(B <= 2.8e+81) && (B <= 9.8e+101))) {
		tmp = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.55e-256:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif (B <= 8.6e-290) or (not (B <= 2.8e+81) and (B <= 9.8e+101)):
		tmp = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.55e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif ((B <= 8.6e-290) || (!(B <= 2.8e+81) && (B <= 9.8e+101)))
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.55e-256)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif ((B <= 8.6e-290) || (~((B <= 2.8e+81)) && (B <= 9.8e+101)))
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	else
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.55e-256], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 8.6e-290], And[N[Not[LessEqual[B, 2.8e+81]], $MachinePrecision], LessEqual[B, 9.8e+101]]], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.55000000000000005e-256

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   if -2.55000000000000005e-256 < B < 8.6000000000000004e-290 or 2.79999999999999995e81 < B < 9.79999999999999965e101

   1. Initial program 45.9%

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

   3. Simplified 46.3%

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

      1. clear-num 46.3%

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

      2. inv-pow 46.3%

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

   5. Applied egg-rr 46.3%

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

      1. unpow-1 46.3%

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

      2. associate--r+ 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in B around 0 66.9%

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

   9. Taylor expanded in C around -inf 68.2%

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

       1. associate-*r/ 67.9%

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

       2. associate-*r/ 67.9%

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

       3. mul-1-neg 67.9%

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

       4. sub-neg 67.9%

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

   11. Simplified 67.9%

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

   12. Taylor expanded in B around 0 68.2%

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

       1. sub-neg 68.2%

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

       2. mul-1-neg 68.2%

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

       3. associate-*r/ 68.2%

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

       4. mul-1-neg 68.2%

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

       5. sub-neg 68.2%

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

       6. *-commutative 68.2%

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

       7. associate-*r/ 68.1%

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

   14. Simplified 68.1%

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

   if 8.6000000000000004e-290 < B < 2.79999999999999995e81 or 9.79999999999999965e101 < B

   1. Initial program 60.2%

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

      1. associate-*r/ 60.2%

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

      2. associate-*l/ 60.2%

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

      3. *-un-lft-identity 60.2%

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

      4. associate--l- 59.1%

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

      5. unpow2 59.1%

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

      6. pow2 59.1%

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

      7. hypot-def 79.1%

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

   3. Applied egg-rr 79.1%

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

   4. Taylor expanded in B around inf 68.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.55 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-290} \lor \neg \left(B \leq 2.8 \cdot 10^{+81}\right) \land B \leq 9.8 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 45.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.4 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -5.4e-28)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -6e-256)
       t_0
       (if (<= B 4.5e-290)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 2.2e-217) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -5.4e-28) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6e-256) {
		tmp = t_0;
	} else if (B <= 4.5e-290) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.2e-217) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -5.4e-28) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6e-256) {
		tmp = t_0;
	} else if (B <= 4.5e-290) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.2e-217) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -5.4e-28:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6e-256:
		tmp = t_0
	elif B <= 4.5e-290:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.2e-217:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -5.4e-28)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6e-256)
		tmp = t_0;
	elseif (B <= 4.5e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.2e-217)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -5.4e-28)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6e-256)
		tmp = t_0;
	elseif (B <= 4.5e-290)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.2e-217)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.4e-28], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6e-256], t$95$0, If[LessEqual[B, 4.5e-290], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-217], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -5.3999999999999998e-28

   1. Initial program 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in B around -inf 68.8%

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

   if -5.3999999999999998e-28 < B < -5.9999999999999996e-256 or 4.5e-290 < B < 2.19999999999999982e-217

   1. Initial program 67.3%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in C around -inf 45.9%

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

   if -5.9999999999999996e-256 < B < 4.5e-290

   1. Initial program 49.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in C around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. distribute-frac-neg 54.6%

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

      6. metadata-eval 54.6%

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

   6. Simplified 54.6%

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

   if 2.19999999999999982e-217 < B

   1. Initial program 55.1%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in B around inf 51.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 50.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.2e-259)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 1.12e-290)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 2.2e-217)
       (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-259) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 1.12e-290) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.2e-217) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-259) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 1.12e-290) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.2e-217) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.2e-259:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 1.12e-290:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.2e-217:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.2e-259)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 1.12e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.2e-217)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.2e-259)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 1.12e-290)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.2e-217)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.2e-259], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.12e-290], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-217], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $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 < -5.20000000000000002e-259

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in C around inf 69.7%

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

   if -5.20000000000000002e-259 < B < 1.12e-290

   1. Initial program 49.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in C around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. distribute-frac-neg 54.6%

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

      6. metadata-eval 54.6%

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

   6. Simplified 54.6%

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

   if 1.12e-290 < B < 2.19999999999999982e-217

   1. Initial program 89.7%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in C around -inf 67.6%

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

   if 2.19999999999999982e-217 < B

   1. Initial program 55.1%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in B around inf 51.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-259}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 51.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.3e-256)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B -1.55e-281)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 9e-47)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.3e-256) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= -1.55e-281) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 9e-47) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.3e-256) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= -1.55e-281) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 9e-47) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.3e-256:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= -1.55e-281:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 9e-47:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.3e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= -1.55e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 9e-47)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.3e-256)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= -1.55e-281)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 9e-47)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.3e-256], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.55e-281], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-47], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $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 < -1.3e-256

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in C around inf 69.7%

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

   if -1.3e-256 < B < -1.5500000000000001e-281

   1. Initial program 34.6%

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

   3. Simplified 22.5%

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

   4. Taylor expanded in C around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-rgt1-in 83.0%

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

      3. metadata-eval 83.0%

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

      4. mul0-lft 83.0%

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

      5. distribute-frac-neg 83.0%

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

      6. metadata-eval 83.0%

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

   6. Simplified 83.0%

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

   if -1.5500000000000001e-281 < B < 9e-47

   1. Initial program 67.3%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in A around inf 46.7%

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

      1. associate-*r/ 46.7%

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

      2. *-commutative 46.7%

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

   6. Simplified 46.7%

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

   if 9e-47 < B

   1. Initial program 52.2%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in B around inf 57.5%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 66.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.2e-258)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -2.1e-281)
       (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.2e-258) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -2.1e-281) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.2e-258) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -2.1e-281) {
		tmp = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.2e-258:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -2.1e-281:
		tmp = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.2e-258)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -2.1e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.2e-258)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -2.1e-281)
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.2e-258], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.1e-281], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.2000000000000001e-258

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   if -1.2000000000000001e-258 < B < -2.0999999999999999e-281

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

      1. clear-num 34.6%

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

      2. inv-pow 34.6%

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

   5. Applied egg-rr 34.6%

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

      1. unpow-1 34.6%

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

      2. associate--r+ 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in B around 0 94.5%

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

   9. Taylor expanded in C around -inf 98.7%

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

       1. associate-*r/ 98.8%

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

       2. associate-*r/ 98.9%

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

       3. mul-1-neg 98.9%

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

       4. sub-neg 98.9%

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

   11. Simplified 98.9%

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

   12. Taylor expanded in B around 0 98.7%

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

       1. sub-neg 98.7%

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

       2. mul-1-neg 98.7%

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

       3. associate-*r/ 98.7%

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

       4. mul-1-neg 98.7%

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

       5. sub-neg 98.7%

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

       6. *-commutative 98.7%

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

       7. associate-*r/ 98.7%

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

   14. Simplified 98.7%

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

   if -2.0999999999999999e-281 < B

   1. Initial program 58.2%

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

   3. Simplified 57.4%

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

   4. Taylor expanded in B around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. associate--r+ 68.7%

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

      3. div-sub 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 12: 66.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -4.2e-256)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -1.5e-281)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -4.2e-256) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -1.5e-281) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -4.2e-256) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -1.5e-281) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -4.2e-256:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -1.5e-281:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -4.2e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -1.5e-281)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -4.2e-256)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -1.5e-281)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -4.2e-256], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.5e-281], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.20000000000000005e-256

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   if -4.20000000000000005e-256 < B < -1.49999999999999987e-281

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in B around 0 98.8%

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

      1. associate-*r/ 98.9%

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

   6. Simplified 98.9%

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

   if -1.49999999999999987e-281 < B

   1. Initial program 58.2%

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

   3. Simplified 57.4%

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

   4. Taylor expanded in B around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. associate--r+ 68.7%

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

      3. div-sub 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 13: 66.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.52 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.52e-257)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B -1.35e-281)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (/ (* 180.0 (atan (/ (- (- C B) A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.52e-257) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= -1.35e-281) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 * atan((((C - B) - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.52e-257) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= -1.35e-281) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 * Math.atan((((C - B) - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.52e-257:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= -1.35e-281:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 * math.atan((((C - B) - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.52e-257)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= -1.35e-281)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - B) - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.52e-257)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= -1.35e-281)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 * atan((((C - B) - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.52e-257], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.35e-281], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.5199999999999999e-257

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   if -1.5199999999999999e-257 < B < -1.34999999999999995e-281

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in B around 0 98.8%

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

      1. associate-*r/ 98.9%

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

   6. Simplified 98.9%

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

   if -1.34999999999999995e-281 < B

   1. Initial program 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*l/ 58.2%

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

      3. *-un-lft-identity 58.2%

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

      4. associate--l- 57.4%

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

      5. unpow2 57.4%

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

      6. pow2 57.4%

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

      7. hypot-def 73.5%

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

   3. Applied egg-rr 73.5%

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

   4. Taylor expanded in B around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   6. Simplified 69.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.52 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 55.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.8e-258)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 9.6e-290)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (/ (* 180.0 (atan (/ (- C B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-258) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 9.6e-290) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-258) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 9.6e-290) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.8e-258:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 9.6e-290:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.8e-258)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 9.6e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.8e-258)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 9.6e-290)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.8e-258], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.6e-290], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.79999999999999989e-258

   1. Initial program 60.1%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in C around inf 69.7%

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

   if -1.79999999999999989e-258 < B < 9.6000000000000002e-290

   1. Initial program 49.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in C around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. distribute-frac-neg 54.6%

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

      6. metadata-eval 54.6%

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

   6. Simplified 54.6%

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

   if 9.6000000000000002e-290 < B

   1. Initial program 58.0%

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

      1. associate-*r/ 58.0%

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

      2. associate-*l/ 58.0%

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

      3. *-un-lft-identity 58.0%

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

      4. associate--l- 57.1%

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

      5. unpow2 57.1%

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

      6. pow2 57.1%

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

      7. hypot-def 75.1%

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

   3. Applied egg-rr 75.1%

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

   4. Taylor expanded in B around inf 63.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 44.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-144}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.9e-144)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.5e-227)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.9e-144) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.5e-227) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.9e-144) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.5e-227) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.9e-144:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.5e-227:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.9e-144)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.5e-227)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.9e-144)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.5e-227)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.9e-144], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-227], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.90000000000000015e-144

   1. Initial program 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in B around -inf 56.8%

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

   if -3.90000000000000015e-144 < B < 8.50000000000000018e-227

   1. Initial program 63.1%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in C around inf 35.4%

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

      1. mul-1-neg 35.4%

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

      2. distribute-rgt1-in 35.4%

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

      3. metadata-eval 35.4%

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

      4. mul0-lft 35.4%

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

      5. distribute-frac-neg 35.4%

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

      6. metadata-eval 35.4%

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

   6. Simplified 35.4%

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

   if 8.50000000000000018e-227 < B

   1. Initial program 56.0%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in B around inf 51.1%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-144}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 40.1% accurate, 2.5× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.999999999999969e-311

   1. Initial program 59.9%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in B around -inf 45.8%

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

   if -9.999999999999969e-311 < B

   1. Initial program 56.4%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in B around inf 46.8%

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

4. Final simplification 46.2%

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

Alternative 17: 20.6% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.4%

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

3. Simplified 57.6%

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

4. Taylor expanded in B around inf 21.3%

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

5. Final simplification 21.3%

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

Reproduce

herbie shell --seed 2023293 
(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)))