ABCF->ab-angle angle

Percentage Accurate: 53.8% → 83.9%

Time: 27.1s

Alternatives: 30

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: 53.8% 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: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_1 \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_0 \cdot {t_0}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B))))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.5)
     t_0
     (if (<= t_1 5e-7)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
       (cbrt (* t_0 (pow t_0 2.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 5e-7) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = cbrt((t_0 * pow(t_0, 2.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 5e-7) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = Math.cbrt((t_0 * Math.pow(t_0, 2.0)));
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -0.5)
		tmp = t_0;
	elseif (t_1 <= 5e-7)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = cbrt(Float64(t_0 * (t_0 ^ 2.0)));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = 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[LessEqual[t$95$1, -0.5], t$95$0, If[LessEqual[t$95$1, 5e-7], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$0 * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5

   1. Initial program 58.7%

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

   3. Simplified 82.4%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 4.99999999999999977e-7

   1. Initial program 21.6%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in B around 0 99.2%

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

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

   if 4.99999999999999977e-7 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 59.1%

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

   3. Simplified 85.5%

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

      1. add-cbrt-cube 86.2%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\right) \cdot \left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\right)\right) \cdot \left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\right)}} \]

      2. pow2 86.2%

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

   5. Applied egg-rr 86.2%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\right) \cdot {\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\right)}^{2}}\\ \end{array} \]

Alternative 2: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 (<= t_0 -0.5)
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))
     (if (<= t_0 5e-7)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
       (/ (* 180.0 (atan (/ (- C (+ A (hypot (- A C) B))) B))) PI)))))

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 <= -0.5) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	} else if (t_0 <= 5e-7) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 * atan(((C - (A + hypot((A - C), B))) / B))) / ((double) M_PI);
	}
	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 <= -0.5) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	} else if (t_0 <= 5e-7) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 * Math.atan(((C - (A + Math.hypot((A - C), B))) / B))) / Math.PI;
	}
	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 <= -0.5:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	elif t_0 <= 5e-7:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 * math.atan(((C - (A + math.hypot((A - C), B))) / B))) / math.pi
	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 <= -0.5)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	elseif (t_0 <= 5e-7)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + hypot(Float64(A - C), B))) / B))) / pi);
	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 <= -0.5)
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	elseif (t_0 <= 5e-7)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 * atan(((C - (A + hypot((A - C), B))) / B))) / pi;
	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[LessEqual[t$95$0, -0.5], 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], If[LessEqual[t$95$0, 5e-7], 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[(C - N[(A + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5

   1. Initial program 58.7%

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

   3. Simplified 82.4%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 4.99999999999999977e-7

   1. Initial program 21.6%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in B around 0 99.2%

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

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

   if 4.99999999999999977e-7 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 59.1%

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

      1. associate-*r/ 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-un-lft-identity 59.1%

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

      4. 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 85.5%

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

   3. Applied egg-rr 85.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 75.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -5.4 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -3.9 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;A \leq 29000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= A -5.4e+101)
     t_1
     (if (<= A -3.9e+67)
       t_0
       (if (<= A -3.2e+46)
         t_1
         (if (<= A 2.4e-78)
           t_0
           (if (<= A 5.9e-52)
             (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
             (if (<= A 29000000000.0)
               t_0
               (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	double t_1 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -5.4e+101) {
		tmp = t_1;
	} else if (A <= -3.9e+67) {
		tmp = t_0;
	} else if (A <= -3.2e+46) {
		tmp = t_1;
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 5.9e-52) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else if (A <= 29000000000.0) {
		tmp = t_0;
	} 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 t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -5.4e+101) {
		tmp = t_1;
	} else if (A <= -3.9e+67) {
		tmp = t_0;
	} else if (A <= -3.2e+46) {
		tmp = t_1;
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 5.9e-52) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else if (A <= 29000000000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if A <= -5.4e+101:
		tmp = t_1
	elif A <= -3.9e+67:
		tmp = t_0
	elif A <= -3.2e+46:
		tmp = t_1
	elif A <= 2.4e-78:
		tmp = t_0
	elif A <= 5.9e-52:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	elif A <= 29000000000.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (A <= -5.4e+101)
		tmp = t_1;
	elseif (A <= -3.9e+67)
		tmp = t_0;
	elseif (A <= -3.2e+46)
		tmp = t_1;
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 5.9e-52)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	elseif (A <= 29000000000.0)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (A <= -5.4e+101)
		tmp = t_1;
	elseif (A <= -3.9e+67)
		tmp = t_0;
	elseif (A <= -3.2e+46)
		tmp = t_1;
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 5.9e-52)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	elseif (A <= 29000000000.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.4e+101], t$95$1, If[LessEqual[A, -3.9e+67], t$95$0, If[LessEqual[A, -3.2e+46], t$95$1, If[LessEqual[A, 2.4e-78], t$95$0, If[LessEqual[A, 5.9e-52], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 29000000000.0], t$95$0, 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 4 regimes

2. if A < -5.40000000000000012e101 or -3.90000000000000007e67 < A < -3.1999999999999998e46

   1. Initial program 14.3%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in B around 0 84.9%

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

      1. associate-*r/ 84.9%

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

   6. Simplified 84.9%

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

   if -5.40000000000000012e101 < A < -3.90000000000000007e67 or -3.1999999999999998e46 < A < 2.4e-78 or 5.90000000000000019e-52 < A < 2.9e10

   1. Initial program 54.0%

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

   3. Simplified 52.5%

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

   4. Taylor expanded in A around 0 50.8%

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

      1. unpow2 50.8%

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

      2. unpow2 50.8%

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

      3. hypot-def 81.1%

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

   6. Simplified 81.1%

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

   if 2.4e-78 < A < 5.90000000000000019e-52

   1. Initial program 38.5%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in B around 0 48.1%

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

      1. unpow2 48.1%

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

   6. Simplified 48.1%

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

   7. Taylor expanded in C around inf 79.8%

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

      1. associate-*r/ 79.8%

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

   9. Simplified 79.8%

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

   if 2.9e10 < A

   1. Initial program 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in B around -inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. div-sub 90.9%

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

   6. Simplified 90.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -3.9 \cdot 10^{+67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;A \leq 29000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 75.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -3.4 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;A \leq 270000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI))
        (t_1 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= A -3.4e+102)
     t_1
     (if (<= A -1.7e+68)
       t_0
       (if (<= A -2.3e+48)
         t_1
         (if (<= A 2.4e-78)
           t_0
           (if (<= A 5.9e-52)
             (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
             (if (<= A 270000000000.0)
               (* 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 t_0 = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	double t_1 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -3.4e+102) {
		tmp = t_1;
	} else if (A <= -1.7e+68) {
		tmp = t_0;
	} else if (A <= -2.3e+48) {
		tmp = t_1;
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 5.9e-52) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else if (A <= 270000000000.0) {
		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 t_0 = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	double t_1 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -3.4e+102) {
		tmp = t_1;
	} else if (A <= -1.7e+68) {
		tmp = t_0;
	} else if (A <= -2.3e+48) {
		tmp = t_1;
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 5.9e-52) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else if (A <= 270000000000.0) {
		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):
	t_0 = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	t_1 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if A <= -3.4e+102:
		tmp = t_1
	elif A <= -1.7e+68:
		tmp = t_0
	elif A <= -2.3e+48:
		tmp = t_1
	elif A <= 2.4e-78:
		tmp = t_0
	elif A <= 5.9e-52:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	elif A <= 270000000000.0:
		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)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi)
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (A <= -3.4e+102)
		tmp = t_1;
	elseif (A <= -1.7e+68)
		tmp = t_0;
	elseif (A <= -2.3e+48)
		tmp = t_1;
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 5.9e-52)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	elseif (A <= 270000000000.0)
		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)
	t_0 = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	t_1 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (A <= -3.4e+102)
		tmp = t_1;
	elseif (A <= -1.7e+68)
		tmp = t_0;
	elseif (A <= -2.3e+48)
		tmp = t_1;
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 5.9e-52)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	elseif (A <= 270000000000.0)
		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_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.4e+102], t$95$1, If[LessEqual[A, -1.7e+68], t$95$0, If[LessEqual[A, -2.3e+48], t$95$1, If[LessEqual[A, 2.4e-78], t$95$0, If[LessEqual[A, 5.9e-52], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 270000000000.0], 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 5 regimes

2. if A < -3.4e102 or -1.70000000000000008e68 < A < -2.3e48

   1. Initial program 14.3%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in B around 0 84.9%

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

      1. associate-*r/ 84.9%

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

   6. Simplified 84.9%

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

   if -3.4e102 < A < -1.70000000000000008e68 or -2.3e48 < A < 2.4e-78

   1. Initial program 53.4%

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

      1. associate-*r/ 53.4%

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

      2. associate-*l/ 53.4%

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

      3. *-un-lft-identity 53.4%

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

      4. associate--l- 51.9%

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

      5. unpow2 51.9%

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

      6. pow2 51.9%

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

      7. hypot-def 81.2%

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

   3. Applied egg-rr 81.2%

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

   4. Taylor expanded in A around 0 50.1%

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

      1. +-commutative 50.1%

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

      2. unpow2 50.1%

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

      3. unpow2 50.1%

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

      4. hypot-def 80.1%

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

   6. Simplified 80.1%

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

   if 2.4e-78 < A < 5.90000000000000019e-52

   1. Initial program 38.5%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in B around 0 48.1%

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

      1. unpow2 48.1%

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

   6. Simplified 48.1%

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

   7. Taylor expanded in C around inf 79.8%

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

      1. associate-*r/ 79.8%

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

   9. Simplified 79.8%

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

   if 5.90000000000000019e-52 < A < 2.7e11

   1. Initial program 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in A around 0 65.2%

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

      1. unpow2 65.2%

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

      2. unpow2 65.2%

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

      3. hypot-def 100.0%

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

   6. Simplified 100.0%

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

   if 2.7e11 < A

   1. Initial program 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in B around -inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. div-sub 90.9%

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

   6. Simplified 90.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;A \leq 270000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 81.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -5.2 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= A -5.2e+101)
     t_0
     (if (<= A -2.8e+67)
       (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
       (if (<= A -5.8e+34)
         t_0
         (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -5.2e+101) {
		tmp = t_0;
	} else if (A <= -2.8e+67) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else if (A <= -5.8e+34) {
		tmp = t_0;
	} 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 t_0 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -5.2e+101) {
		tmp = t_0;
	} else if (A <= -2.8e+67) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else if (A <= -5.8e+34) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if A <= -5.2e+101:
		tmp = t_0
	elif A <= -2.8e+67:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	elif A <= -5.8e+34:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (A <= -5.2e+101)
		tmp = t_0;
	elseif (A <= -2.8e+67)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	elseif (A <= -5.8e+34)
		tmp = t_0;
	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)
	t_0 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (A <= -5.2e+101)
		tmp = t_0;
	elseif (A <= -2.8e+67)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	elseif (A <= -5.8e+34)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.2e+101], t$95$0, If[LessEqual[A, -2.8e+67], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -5.8e+34], t$95$0, 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 3 regimes

2. if A < -5.2e101 or -2.7999999999999998e67 < A < -5.8000000000000003e34

   1. Initial program 14.3%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in B around 0 84.9%

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

      1. associate-*r/ 84.9%

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

   6. Simplified 84.9%

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

   if -5.2e101 < A < -2.7999999999999998e67

   1. Initial program 52.6%

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

      1. associate-*r/ 52.7%

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

      2. associate-*l/ 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. associate--l- 38.8%

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

      5. unpow2 38.8%

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

      6. pow2 38.8%

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

      7. hypot-def 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in A around 0 38.8%

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

      1. +-commutative 38.8%

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

      2. unpow2 38.8%

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

      3. unpow2 38.8%

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

      4. hypot-def 86.2%

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

   6. Simplified 86.2%

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

   if -5.8000000000000003e34 < A

   1. Initial program 63.4%

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

   3. Simplified 85.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 81.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;A \leq -7 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{+67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= A -7e+101)
     t_0
     (if (<= A -2.25e+67)
       (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
       (if (<= A -7.5e+42)
         t_0
         (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -7e+101) {
		tmp = t_0;
	} else if (A <= -2.25e+67) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else if (A <= -7.5e+42) {
		tmp = t_0;
	} 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 t_0 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (A <= -7e+101) {
		tmp = t_0;
	} else if (A <= -2.25e+67) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else if (A <= -7.5e+42) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if A <= -7e+101:
		tmp = t_0
	elif A <= -2.25e+67:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	elif A <= -7.5e+42:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (A <= -7e+101)
		tmp = t_0;
	elseif (A <= -2.25e+67)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	elseif (A <= -7.5e+42)
		tmp = t_0;
	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)
	t_0 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (A <= -7e+101)
		tmp = t_0;
	elseif (A <= -2.25e+67)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	elseif (A <= -7.5e+42)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7e+101], t$95$0, If[LessEqual[A, -2.25e+67], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -7.5e+42], t$95$0, 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 3 regimes

2. if A < -7.00000000000000046e101 or -2.2499999999999999e67 < A < -7.50000000000000041e42

   1. Initial program 14.3%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in B around 0 84.9%

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

      1. associate-*r/ 84.9%

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

   6. Simplified 84.9%

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

   if -7.00000000000000046e101 < A < -2.2499999999999999e67

   1. Initial program 52.6%

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

      1. associate-*r/ 52.7%

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

      2. associate-*l/ 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. associate--l- 38.8%

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

      5. unpow2 38.8%

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

      6. pow2 38.8%

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

      7. hypot-def 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in A around 0 38.8%

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

      1. +-commutative 38.8%

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

      2. unpow2 38.8%

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

      3. unpow2 38.8%

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

      4. hypot-def 86.2%

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

   6. Simplified 86.2%

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

   if -7.50000000000000041e42 < A

   1. Initial program 63.4%

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

   3. Simplified 85.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{+101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{+67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 7: 79.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -8 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{+100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -8e-45)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 2.1e+100)
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI))
     (/ (* 180.0 (atan (/ (* B 0.5) (- A C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -8e-45) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 2.1e+100) {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -8e-45) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 2.1e+100) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B * 0.5) / (A - C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -8e-45:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 2.1e+100:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B * 0.5) / (A - C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -8e-45)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 2.1e+100)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / Float64(A - C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -8e-45)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 2.1e+100)
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	else
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -8e-45], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e+100], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -7.99999999999999987e-45

   1. Initial program 80.9%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in A around 0 79.3%

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

      1. unpow2 79.3%

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

      2. unpow2 79.3%

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

      3. hypot-def 87.5%

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

   6. Simplified 87.5%

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

   if -7.99999999999999987e-45 < C < 2.0999999999999999e100

   1. Initial program 52.1%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in C around 0 49.9%

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

      1. associate-*r/ 49.9%

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

      2. mul-1-neg 49.9%

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

      3. +-commutative 49.9%

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

      4. unpow2 49.9%

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

      5. unpow2 49.9%

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

      6. hypot-def 75.4%

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

   6. Simplified 75.4%

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

   if 2.0999999999999999e100 < C

   1. Initial program 21.0%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around 0 63.4%

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

      1. unpow2 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in C around -inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l/ 71.5%

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

      3. associate-*r/ 71.5%

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

      4. mul-1-neg 71.5%

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

      5. sub-neg 71.5%

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

   9. Simplified 71.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -8 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{+100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \]

Alternative 8: 79.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.9e-45)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 8.5e+99)
     (* (/ 180.0 PI) (atan (/ (- (- A) (hypot B A)) B)))
     (/ (* 180.0 (atan (/ (* B 0.5) (- A C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.9e-45) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 8.5e+99) {
		tmp = (180.0 / ((double) M_PI)) * atan(((-A - hypot(B, A)) / B));
	} else {
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.9e-45) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 8.5e+99) {
		tmp = (180.0 / Math.PI) * Math.atan(((-A - Math.hypot(B, A)) / B));
	} else {
		tmp = (180.0 * Math.atan(((B * 0.5) / (A - C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.9e-45:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 8.5e+99:
		tmp = (180.0 / math.pi) * math.atan(((-A - math.hypot(B, A)) / B))
	else:
		tmp = (180.0 * math.atan(((B * 0.5) / (A - C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.9e-45)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 8.5e+99)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / Float64(A - C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.9e-45)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 8.5e+99)
		tmp = (180.0 / pi) * atan(((-A - hypot(B, A)) / B));
	else
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.9e-45], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.5e+99], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.89999999999999999e-45

   1. Initial program 80.9%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in A around 0 79.3%

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

      1. unpow2 79.3%

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

      2. unpow2 79.3%

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

      3. hypot-def 87.5%

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

   6. Simplified 87.5%

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

   if -1.89999999999999999e-45 < C < 8.49999999999999984e99

   1. Initial program 52.1%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in C around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. +-commutative 49.9%

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

      3. unpow2 49.9%

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

      4. unpow2 49.9%

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

      5. hypot-def 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in B around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. mul-1-neg 75.4%

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

      3. distribute-frac-neg 75.4%

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

      4. associate-/l* 75.4%

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

      5. associate-/r/ 75.4%

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

      6. neg-sub0 75.4%

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

      7. associate--r+ 75.4%

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

      8. neg-sub0 75.4%

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

   9. Simplified 75.4%

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

   if 8.49999999999999984e99 < C

   1. Initial program 21.0%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around 0 63.4%

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

      1. unpow2 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in C around -inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l/ 71.5%

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

      3. associate-*r/ 71.5%

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

      4. mul-1-neg 71.5%

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

      5. sub-neg 71.5%

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

   9. Simplified 71.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \]

Alternative 9: 79.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8 \cdot 10^{+99}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.85e-41)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 8e+99)
     (/ (* 180.0 (atan (/ (- (- A) (hypot A B)) B))) PI)
     (/ (* 180.0 (atan (/ (* B 0.5) (- A C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.85e-41) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 8e+99) {
		tmp = (180.0 * atan(((-A - hypot(A, B)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.85e-41) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 8e+99) {
		tmp = (180.0 * Math.atan(((-A - Math.hypot(A, B)) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B * 0.5) / (A - C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.85e-41:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 8e+99:
		tmp = (180.0 * math.atan(((-A - math.hypot(A, B)) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B * 0.5) / (A - C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.85e-41)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 8e+99)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / Float64(A - C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.85e-41)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 8e+99)
		tmp = (180.0 * atan(((-A - hypot(A, B)) / B))) / pi;
	else
		tmp = (180.0 * atan(((B * 0.5) / (A - C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.85e-41], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8e+99], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.8500000000000001e-41

   1. Initial program 80.9%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in A around 0 79.3%

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

      1. unpow2 79.3%

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

      2. unpow2 79.3%

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

      3. hypot-def 87.5%

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

   6. Simplified 87.5%

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

   if -1.8500000000000001e-41 < C < 7.9999999999999997e99

   1. Initial program 52.1%

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

      1. associate-*r/ 52.2%

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

      2. associate-*l/ 52.1%

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

      3. *-un-lft-identity 52.1%

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

      4. associate--l- 50.5%

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

      5. unpow2 50.5%

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

      6. pow2 50.5%

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

      7. hypot-def 70.8%

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

   3. Applied egg-rr 70.8%

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

   4. Taylor expanded in C around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unpow2 49.9%

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

      3. unpow2 49.9%

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

      4. hypot-def 75.4%

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

   6. Simplified 75.4%

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

   if 7.9999999999999997e99 < C

   1. Initial program 21.0%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around 0 63.4%

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

      1. unpow2 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in C around -inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l/ 71.5%

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

      3. associate-*r/ 71.5%

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

      4. mul-1-neg 71.5%

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

      5. sub-neg 71.5%

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

   9. Simplified 71.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8 \cdot 10^{+99}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\pi}\\ \end{array} \]

Alternative 10: 65.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -5.5 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.06 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.85 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_1 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -5.5e-39)
     t_2
     (if (<= B -4.1e-132)
       t_0
       (if (<= B -2.06e-162)
         t_2
         (if (<= B -4.5e-201)
           t_0
           (if (<= B 2.85e-272)
             t_2
             (if (<= B 1.3e-251)
               t_0
               (* 180.0 (/ (atan (+ t_1 -1.0)) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -5.5e-39) {
		tmp = t_2;
	} else if (B <= -4.1e-132) {
		tmp = t_0;
	} else if (B <= -2.06e-162) {
		tmp = t_2;
	} else if (B <= -4.5e-201) {
		tmp = t_0;
	} else if (B <= 2.85e-272) {
		tmp = t_2;
	} else if (B <= 1.3e-251) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((t_1 + -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((B * (0.5 / (A - C)))) / Math.PI);
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -5.5e-39) {
		tmp = t_2;
	} else if (B <= -4.1e-132) {
		tmp = t_0;
	} else if (B <= -2.06e-162) {
		tmp = t_2;
	} else if (B <= -4.5e-201) {
		tmp = t_0;
	} else if (B <= 2.85e-272) {
		tmp = t_2;
	} else if (B <= 1.3e-251) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -5.5e-39:
		tmp = t_2
	elif B <= -4.1e-132:
		tmp = t_0
	elif B <= -2.06e-162:
		tmp = t_2
	elif B <= -4.5e-201:
		tmp = t_0
	elif B <= 2.85e-272:
		tmp = t_2
	elif B <= 1.3e-251:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -5.5e-39)
		tmp = t_2;
	elseif (B <= -4.1e-132)
		tmp = t_0;
	elseif (B <= -2.06e-162)
		tmp = t_2;
	elseif (B <= -4.5e-201)
		tmp = t_0;
	elseif (B <= 2.85e-272)
		tmp = t_2;
	elseif (B <= 1.3e-251)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -5.5e-39)
		tmp = t_2;
	elseif (B <= -4.1e-132)
		tmp = t_0;
	elseif (B <= -2.06e-162)
		tmp = t_2;
	elseif (B <= -4.5e-201)
		tmp = t_0;
	elseif (B <= 2.85e-272)
		tmp = t_2;
	elseif (B <= 1.3e-251)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.5e-39], t$95$2, If[LessEqual[B, -4.1e-132], t$95$0, If[LessEqual[B, -2.06e-162], t$95$2, If[LessEqual[B, -4.5e-201], t$95$0, If[LessEqual[B, 2.85e-272], t$95$2, If[LessEqual[B, 1.3e-251], t$95$0, N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.50000000000000018e-39 or -4.10000000000000007e-132 < B < -2.06e-162 or -4.5000000000000002e-201 < B < 2.8499999999999999e-272

   1. Initial program 58.7%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 77.1%

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

   6. Simplified 77.1%

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

   if -5.50000000000000018e-39 < B < -4.10000000000000007e-132 or -2.06e-162 < B < -4.5000000000000002e-201 or 2.8499999999999999e-272 < B < 1.3e-251

   1. Initial program 26.4%

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

   3. Simplified 31.7%

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

   4. Taylor expanded in B around 0 50.0%

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

      1. unpow2 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in C around -inf 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 84.5%

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

      3. associate-*r/ 84.5%

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

      4. mul-1-neg 84.5%

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

      5. sub-neg 84.5%

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

   9. Simplified 84.5%

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

   10. Taylor expanded in B around 0 84.6%

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

       1. associate-*r/ 84.6%

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

       2. associate-*l/ 84.5%

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

       3. *-commutative 84.5%

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

   12. Simplified 84.5%

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

   if 1.3e-251 < B

   1. Initial program 55.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in B around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. associate--r+ 71.6%

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

      3. div-sub 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.1 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.06 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.85 \cdot 10^{-272}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 11: 65.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_1 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -5.7e-39)
     t_2
     (if (<= B -2.8e-132)
       t_0
       (if (<= B -1.25e-160)
         t_2
         (if (<= B -1.65e-198)
           t_0
           (if (<= B 9e-271)
             t_2
             (if (<= B 3.5e-251)
               (* 180.0 (/ (atan (/ (* B -0.5) (- C A))) PI))
               (* 180.0 (/ (atan (+ t_1 -1.0)) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -5.7e-39) {
		tmp = t_2;
	} else if (B <= -2.8e-132) {
		tmp = t_0;
	} else if (B <= -1.25e-160) {
		tmp = t_2;
	} else if (B <= -1.65e-198) {
		tmp = t_0;
	} else if (B <= 9e-271) {
		tmp = t_2;
	} else if (B <= 3.5e-251) {
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((t_1 + -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((B * (0.5 / (A - C)))) / Math.PI);
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -5.7e-39) {
		tmp = t_2;
	} else if (B <= -2.8e-132) {
		tmp = t_0;
	} else if (B <= -1.25e-160) {
		tmp = t_2;
	} else if (B <= -1.65e-198) {
		tmp = t_0;
	} else if (B <= 9e-271) {
		tmp = t_2;
	} else if (B <= 3.5e-251) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / (C - A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -5.7e-39:
		tmp = t_2
	elif B <= -2.8e-132:
		tmp = t_0
	elif B <= -1.25e-160:
		tmp = t_2
	elif B <= -1.65e-198:
		tmp = t_0
	elif B <= 9e-271:
		tmp = t_2
	elif B <= 3.5e-251:
		tmp = 180.0 * (math.atan(((B * -0.5) / (C - A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -5.7e-39)
		tmp = t_2;
	elseif (B <= -2.8e-132)
		tmp = t_0;
	elseif (B <= -1.25e-160)
		tmp = t_2;
	elseif (B <= -1.65e-198)
		tmp = t_0;
	elseif (B <= 9e-271)
		tmp = t_2;
	elseif (B <= 3.5e-251)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -5.7e-39)
		tmp = t_2;
	elseif (B <= -2.8e-132)
		tmp = t_0;
	elseif (B <= -1.25e-160)
		tmp = t_2;
	elseif (B <= -1.65e-198)
		tmp = t_0;
	elseif (B <= 9e-271)
		tmp = t_2;
	elseif (B <= 3.5e-251)
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / pi);
	else
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.7e-39], t$95$2, If[LessEqual[B, -2.8e-132], t$95$0, If[LessEqual[B, -1.25e-160], t$95$2, If[LessEqual[B, -1.65e-198], t$95$0, If[LessEqual[B, 9e-271], t$95$2, If[LessEqual[B, 3.5e-251], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -5.6999999999999997e-39 or -2.80000000000000002e-132 < B < -1.24999999999999999e-160 or -1.65e-198 < B < 8.9999999999999995e-271

   1. Initial program 58.7%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 77.1%

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

   6. Simplified 77.1%

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

   if -5.6999999999999997e-39 < B < -2.80000000000000002e-132 or -1.24999999999999999e-160 < B < -1.65e-198

   1. Initial program 23.8%

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

   3. Simplified 31.3%

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

   4. Taylor expanded in B around 0 58.0%

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

      1. unpow2 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in C around -inf 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 84.2%

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

      3. associate-*r/ 84.2%

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

      4. mul-1-neg 84.2%

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

      5. sub-neg 84.2%

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

   9. Simplified 84.2%

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

   10. Taylor expanded in B around 0 84.3%

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

       1. associate-*r/ 84.3%

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

       2. associate-*l/ 84.3%

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

       3. *-commutative 84.3%

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

   12. Simplified 84.3%

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

   if 8.9999999999999995e-271 < B < 3.50000000000000034e-251

   1. Initial program 35.5%

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

   3. Simplified 33.0%

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

   4. Taylor expanded in B around 0 21.6%

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

      1. unpow2 21.6%

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

   6. Simplified 21.6%

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

   7. Taylor expanded in B around 0 85.9%

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

      1. sub-neg 85.9%

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

      2. mul-1-neg 85.9%

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

      3. associate-*r/ 85.9%

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

      4. mul-1-neg 85.9%

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

      5. sub-neg 85.9%

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

   9. Simplified 85.9%

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

   if 3.50000000000000034e-251 < B

   1. Initial program 55.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in B around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. associate--r+ 71.6%

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

      3. div-sub 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.7 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.65 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-271}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 12: 65.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-199}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_1 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -6.8e-39)
     t_2
     (if (<= B -3.6e-132)
       t_0
       (if (<= B -1.8e-160)
         t_2
         (if (<= B -8.5e-199)
           t_0
           (if (<= B 3.8e-273)
             t_2
             (if (<= B 1.5e-250)
               (* 180.0 (/ (atan (/ (* B -0.5) (- C A))) PI))
               (* (/ 180.0 PI) (atan (+ t_1 -1.0)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -6.8e-39) {
		tmp = t_2;
	} else if (B <= -3.6e-132) {
		tmp = t_0;
	} else if (B <= -1.8e-160) {
		tmp = t_2;
	} else if (B <= -8.5e-199) {
		tmp = t_0;
	} else if (B <= 3.8e-273) {
		tmp = t_2;
	} else if (B <= 1.5e-250) {
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_1 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -6.8e-39) {
		tmp = t_2;
	} else if (B <= -3.6e-132) {
		tmp = t_0;
	} else if (B <= -1.8e-160) {
		tmp = t_2;
	} else if (B <= -8.5e-199) {
		tmp = t_0;
	} else if (B <= 3.8e-273) {
		tmp = t_2;
	} else if (B <= 1.5e-250) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / (C - A))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_1 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -6.8e-39:
		tmp = t_2
	elif B <= -3.6e-132:
		tmp = t_0
	elif B <= -1.8e-160:
		tmp = t_2
	elif B <= -8.5e-199:
		tmp = t_0
	elif B <= 3.8e-273:
		tmp = t_2
	elif B <= 1.5e-250:
		tmp = 180.0 * (math.atan(((B * -0.5) / (C - A))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((t_1 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -6.8e-39)
		tmp = t_2;
	elseif (B <= -3.6e-132)
		tmp = t_0;
	elseif (B <= -1.8e-160)
		tmp = t_2;
	elseif (B <= -8.5e-199)
		tmp = t_0;
	elseif (B <= 3.8e-273)
		tmp = t_2;
	elseif (B <= 1.5e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_1 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -6.8e-39)
		tmp = t_2;
	elseif (B <= -3.6e-132)
		tmp = t_0;
	elseif (B <= -1.8e-160)
		tmp = t_2;
	elseif (B <= -8.5e-199)
		tmp = t_0;
	elseif (B <= 3.8e-273)
		tmp = t_2;
	elseif (B <= 1.5e-250)
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / pi);
	else
		tmp = (180.0 / pi) * atan((t_1 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.8e-39], t$95$2, If[LessEqual[B, -3.6e-132], t$95$0, If[LessEqual[B, -1.8e-160], t$95$2, If[LessEqual[B, -8.5e-199], t$95$0, If[LessEqual[B, 3.8e-273], t$95$2, If[LessEqual[B, 1.5e-250], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.7999999999999998e-39 or -3.60000000000000007e-132 < B < -1.7999999999999999e-160 or -8.4999999999999994e-199 < B < 3.8000000000000004e-273

   1. Initial program 58.7%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 77.1%

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

   6. Simplified 77.1%

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

   if -6.7999999999999998e-39 < B < -3.60000000000000007e-132 or -1.7999999999999999e-160 < B < -8.4999999999999994e-199

   1. Initial program 23.8%

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

   3. Simplified 31.3%

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

   4. Taylor expanded in B around 0 58.0%

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

      1. unpow2 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in C around -inf 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 84.2%

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

      3. associate-*r/ 84.2%

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

      4. mul-1-neg 84.2%

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

      5. sub-neg 84.2%

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

   9. Simplified 84.2%

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

   10. Taylor expanded in B around 0 84.3%

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

       1. associate-*r/ 84.3%

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

       2. associate-*l/ 84.3%

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

       3. *-commutative 84.3%

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

   12. Simplified 84.3%

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

   if 3.8000000000000004e-273 < B < 1.50000000000000008e-250

   1. Initial program 35.5%

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

   3. Simplified 33.0%

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

   4. Taylor expanded in B around 0 21.6%

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

      1. unpow2 21.6%

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

   6. Simplified 21.6%

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

   7. Taylor expanded in B around 0 85.9%

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

      1. sub-neg 85.9%

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

      2. mul-1-neg 85.9%

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

      3. associate-*r/ 85.9%

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

      4. mul-1-neg 85.9%

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

      5. sub-neg 85.9%

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

   9. Simplified 85.9%

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

   if 1.50000000000000008e-250 < B

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-*l/ 55.3%

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

      3. *-un-lft-identity 55.3%

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

      4. associate--l- 54.3%

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

      5. unpow2 54.3%

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

      6. pow2 54.3%

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

      7. hypot-def 77.0%

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

   3. Applied egg-rr 77.0%

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

   4. Taylor expanded in B around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in C around 0 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 13: 65.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.66 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_1 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -1.15e-38)
     t_2
     (if (<= B -4e-132)
       t_0
       (if (<= B -6.2e-161)
         t_2
         (if (<= B -4.8e-201)
           t_0
           (if (<= B 1.66e-273)
             t_2
             (if (<= B 2.2e-251)
               t_0
               (* (/ 180.0 PI) (atan (+ t_1 -1.0)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -1.15e-38) {
		tmp = t_2;
	} else if (B <= -4e-132) {
		tmp = t_0;
	} else if (B <= -6.2e-161) {
		tmp = t_2;
	} else if (B <= -4.8e-201) {
		tmp = t_0;
	} else if (B <= 1.66e-273) {
		tmp = t_2;
	} else if (B <= 2.2e-251) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_1 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -1.15e-38) {
		tmp = t_2;
	} else if (B <= -4e-132) {
		tmp = t_0;
	} else if (B <= -6.2e-161) {
		tmp = t_2;
	} else if (B <= -4.8e-201) {
		tmp = t_0;
	} else if (B <= 1.66e-273) {
		tmp = t_2;
	} else if (B <= 2.2e-251) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_1 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -1.15e-38:
		tmp = t_2
	elif B <= -4e-132:
		tmp = t_0
	elif B <= -6.2e-161:
		tmp = t_2
	elif B <= -4.8e-201:
		tmp = t_0
	elif B <= 1.66e-273:
		tmp = t_2
	elif B <= 2.2e-251:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((t_1 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -1.15e-38)
		tmp = t_2;
	elseif (B <= -4e-132)
		tmp = t_0;
	elseif (B <= -6.2e-161)
		tmp = t_2;
	elseif (B <= -4.8e-201)
		tmp = t_0;
	elseif (B <= 1.66e-273)
		tmp = t_2;
	elseif (B <= 2.2e-251)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_1 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -1.15e-38)
		tmp = t_2;
	elseif (B <= -4e-132)
		tmp = t_0;
	elseif (B <= -6.2e-161)
		tmp = t_2;
	elseif (B <= -4.8e-201)
		tmp = t_0;
	elseif (B <= 1.66e-273)
		tmp = t_2;
	elseif (B <= 2.2e-251)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((t_1 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.15e-38], t$95$2, If[LessEqual[B, -4e-132], t$95$0, If[LessEqual[B, -6.2e-161], t$95$2, If[LessEqual[B, -4.8e-201], t$95$0, If[LessEqual[B, 1.66e-273], t$95$2, If[LessEqual[B, 2.2e-251], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.15000000000000001e-38 or -3.9999999999999999e-132 < B < -6.1999999999999997e-161 or -4.80000000000000018e-201 < B < 1.65999999999999995e-273

   1. Initial program 58.7%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 77.1%

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

   6. Simplified 77.1%

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

   if -1.15000000000000001e-38 < B < -3.9999999999999999e-132 or -6.1999999999999997e-161 < B < -4.80000000000000018e-201 or 1.65999999999999995e-273 < B < 2.2e-251

   1. Initial program 26.4%

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

   3. Simplified 31.7%

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

   4. Taylor expanded in B around 0 84.8%

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

      1. associate-*r/ 84.8%

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

   6. Simplified 84.8%

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

   if 2.2e-251 < B

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-*l/ 55.3%

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

      3. *-un-lft-identity 55.3%

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

      4. associate--l- 54.3%

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

      5. unpow2 54.3%

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

      6. pow2 54.3%

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

      7. hypot-def 77.0%

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

   3. Applied egg-rr 77.0%

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

   4. Taylor expanded in B around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in C around 0 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 1.66 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-251}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 14: 65.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(B + C\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B))
        (t_1 (* 180.0 (/ (atan (+ 1.0 t_0)) PI)))
        (t_2 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= B -1.05e-38)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (+ B C) A))) PI))
     (if (<= B -3.3e-132)
       t_2
       (if (<= B -1.02e-161)
         t_1
         (if (<= B -2e-200)
           t_2
           (if (<= B 3.2e-271)
             t_1
             (if (<= B 1.75e-251)
               t_2
               (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	double t_2 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (B <= -1.05e-38) {
		tmp = 180.0 * (atan(((1.0 / B) * ((B + C) - A))) / ((double) M_PI));
	} else if (B <= -3.3e-132) {
		tmp = t_2;
	} else if (B <= -1.02e-161) {
		tmp = t_1;
	} else if (B <= -2e-200) {
		tmp = t_2;
	} else if (B <= 3.2e-271) {
		tmp = t_1;
	} else if (B <= 1.75e-251) {
		tmp = t_2;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	double t_2 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (B <= -1.05e-38) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((B + C) - A))) / Math.PI);
	} else if (B <= -3.3e-132) {
		tmp = t_2;
	} else if (B <= -1.02e-161) {
		tmp = t_1;
	} else if (B <= -2e-200) {
		tmp = t_2;
	} else if (B <= 3.2e-271) {
		tmp = t_1;
	} else if (B <= 1.75e-251) {
		tmp = t_2;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	t_2 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if B <= -1.05e-38:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((B + C) - A))) / math.pi)
	elif B <= -3.3e-132:
		tmp = t_2
	elif B <= -1.02e-161:
		tmp = t_1
	elif B <= -2e-200:
		tmp = t_2
	elif B <= 3.2e-271:
		tmp = t_1
	elif B <= 1.75e-251:
		tmp = t_2
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi))
	t_2 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (B <= -1.05e-38)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(B + C) - A))) / pi));
	elseif (B <= -3.3e-132)
		tmp = t_2;
	elseif (B <= -1.02e-161)
		tmp = t_1;
	elseif (B <= -2e-200)
		tmp = t_2;
	elseif (B <= 3.2e-271)
		tmp = t_1;
	elseif (B <= 1.75e-251)
		tmp = t_2;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	t_1 = 180.0 * (atan((1.0 + t_0)) / pi);
	t_2 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (B <= -1.05e-38)
		tmp = 180.0 * (atan(((1.0 / B) * ((B + C) - A))) / pi);
	elseif (B <= -3.3e-132)
		tmp = t_2;
	elseif (B <= -1.02e-161)
		tmp = t_1;
	elseif (B <= -2e-200)
		tmp = t_2;
	elseif (B <= 3.2e-271)
		tmp = t_1;
	elseif (B <= 1.75e-251)
		tmp = t_2;
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.05e-38], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.3e-132], t$95$2, If[LessEqual[B, -1.02e-161], t$95$1, If[LessEqual[B, -2e-200], t$95$2, If[LessEqual[B, 3.2e-271], t$95$1, If[LessEqual[B, 1.75e-251], t$95$2, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.05000000000000006e-38

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in B around -inf 78.0%

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

   if -1.05000000000000006e-38 < B < -3.2999999999999997e-132 or -1.0199999999999999e-161 < B < -2e-200 or 3.19999999999999978e-271 < B < 1.75000000000000017e-251

   1. Initial program 26.4%

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

   3. Simplified 31.7%

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

   4. Taylor expanded in B around 0 84.8%

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

      1. associate-*r/ 84.8%

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

   6. Simplified 84.8%

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

   if -3.2999999999999997e-132 < B < -1.0199999999999999e-161 or -2e-200 < B < 3.19999999999999978e-271

   1. Initial program 85.0%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in B around -inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. div-sub 74.4%

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

   6. Simplified 74.4%

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

   if 1.75000000000000017e-251 < B

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-*l/ 55.3%

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

      3. *-un-lft-identity 55.3%

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

      4. associate--l- 54.3%

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

      5. unpow2 54.3%

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

      6. pow2 54.3%

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

      7. hypot-def 77.0%

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

   3. Applied egg-rr 77.0%

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

   4. Taylor expanded in B around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in C around 0 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(B + C\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-200}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-251}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 15: 65.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(B + C\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) + 0.5 \cdot \frac{C \cdot C}{B}}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B))
        (t_1 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))))
   (if (<= B -6.8e-39)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (+ B C) A))) PI))
     (if (<= B -2.8e-132)
       t_1
       (if (<= B -4.3e-160)
         (* 180.0 (/ (atan (/ (+ (+ B C) (* 0.5 (/ (* C C) B))) B)) PI))
         (if (<= B -3.4e-202)
           t_1
           (if (<= B 3.6e-270)
             (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
             (if (<= B 1.1e-250)
               t_1
               (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double tmp;
	if (B <= -6.8e-39) {
		tmp = 180.0 * (atan(((1.0 / B) * ((B + C) - A))) / ((double) M_PI));
	} else if (B <= -2.8e-132) {
		tmp = t_1;
	} else if (B <= -4.3e-160) {
		tmp = 180.0 * (atan((((B + C) + (0.5 * ((C * C) / B))) / B)) / ((double) M_PI));
	} else if (B <= -3.4e-202) {
		tmp = t_1;
	} else if (B <= 3.6e-270) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.1e-250) {
		tmp = t_1;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double tmp;
	if (B <= -6.8e-39) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((B + C) - A))) / Math.PI);
	} else if (B <= -2.8e-132) {
		tmp = t_1;
	} else if (B <= -4.3e-160) {
		tmp = 180.0 * (Math.atan((((B + C) + (0.5 * ((C * C) / B))) / B)) / Math.PI);
	} else if (B <= -3.4e-202) {
		tmp = t_1;
	} else if (B <= 3.6e-270) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.1e-250) {
		tmp = t_1;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	tmp = 0
	if B <= -6.8e-39:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((B + C) - A))) / math.pi)
	elif B <= -2.8e-132:
		tmp = t_1
	elif B <= -4.3e-160:
		tmp = 180.0 * (math.atan((((B + C) + (0.5 * ((C * C) / B))) / B)) / math.pi)
	elif B <= -3.4e-202:
		tmp = t_1
	elif B <= 3.6e-270:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.1e-250:
		tmp = t_1
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	tmp = 0.0
	if (B <= -6.8e-39)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(B + C) - A))) / pi));
	elseif (B <= -2.8e-132)
		tmp = t_1;
	elseif (B <= -4.3e-160)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) + Float64(0.5 * Float64(Float64(C * C) / B))) / B)) / pi));
	elseif (B <= -3.4e-202)
		tmp = t_1;
	elseif (B <= 3.6e-270)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.1e-250)
		tmp = t_1;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	t_1 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	tmp = 0.0;
	if (B <= -6.8e-39)
		tmp = 180.0 * (atan(((1.0 / B) * ((B + C) - A))) / pi);
	elseif (B <= -2.8e-132)
		tmp = t_1;
	elseif (B <= -4.3e-160)
		tmp = 180.0 * (atan((((B + C) + (0.5 * ((C * C) / B))) / B)) / pi);
	elseif (B <= -3.4e-202)
		tmp = t_1;
	elseif (B <= 3.6e-270)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.1e-250)
		tmp = t_1;
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.8e-39], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.8e-132], t$95$1, If[LessEqual[B, -4.3e-160], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] + N[(0.5 * N[(N[(C * C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.4e-202], t$95$1, If[LessEqual[B, 3.6e-270], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-250], t$95$1, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -6.7999999999999998e-39

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in B around -inf 78.0%

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

   if -6.7999999999999998e-39 < B < -2.80000000000000002e-132 or -4.30000000000000014e-160 < B < -3.40000000000000012e-202 or 3.5999999999999998e-270 < B < 1.1e-250

   1. Initial program 26.4%

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

   3. Simplified 31.7%

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

   4. Taylor expanded in B around 0 84.8%

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

      1. associate-*r/ 84.8%

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

   6. Simplified 84.8%

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

   if -2.80000000000000002e-132 < B < -4.30000000000000014e-160

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in A around 0 77.5%

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

      1. unpow2 77.5%

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

      2. unpow2 77.5%

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

      3. hypot-def 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in B around -inf 89.7%

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

      1. associate-+r+ 89.7%

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

      2. unpow2 89.7%

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

   9. Simplified 89.7%

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

   if -3.40000000000000012e-202 < B < 3.5999999999999998e-270

   1. Initial program 78.5%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in B around -inf 67.5%

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

      1. associate--l+ 67.5%

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

      2. div-sub 67.7%

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

   6. Simplified 67.7%

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

   if 1.1e-250 < B

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-*l/ 55.3%

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

      3. *-un-lft-identity 55.3%

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

      4. associate--l- 54.3%

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

      5. unpow2 54.3%

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

      6. pow2 54.3%

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

      7. hypot-def 77.0%

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

   3. Applied egg-rr 77.0%

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

   4. Taylor expanded in B around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in C around 0 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(B + C\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) + 0.5 \cdot \frac{C \cdot C}{B}}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-202}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-250}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 16: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.72 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -490000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C B) B))) PI))
        (t_1 (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))))
   (if (<= A -5.5e+102)
     t_1
     (if (<= A -1.72e+68)
       t_0
       (if (<= A -490000000.0)
         t_1
         (if (<= A 1e-236)
           (* 180.0 (/ (atan (/ (+ B C) B)) PI))
           (if (<= A 2.15e-78)
             t_0
             (if (<= A 3e-53)
               (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
               (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	double t_1 = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	double tmp;
	if (A <= -5.5e+102) {
		tmp = t_1;
	} else if (A <= -1.72e+68) {
		tmp = t_0;
	} else if (A <= -490000000.0) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (A <= 2.15e-78) {
		tmp = t_0;
	} else if (A <= 3e-53) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	double t_1 = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -5.5e+102) {
		tmp = t_1;
	} else if (A <= -1.72e+68) {
		tmp = t_0;
	} else if (A <= -490000000.0) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (A <= 2.15e-78) {
		tmp = t_0;
	} else if (A <= 3e-53) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((C - B) / B))) / math.pi
	t_1 = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -5.5e+102:
		tmp = t_1
	elif A <= -1.72e+68:
		tmp = t_0
	elif A <= -490000000.0:
		tmp = t_1
	elif A <= 1e-236:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif A <= 2.15e-78:
		tmp = t_0
	elif A <= 3e-53:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi)
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))))
	tmp = 0.0
	if (A <= -5.5e+102)
		tmp = t_1;
	elseif (A <= -1.72e+68)
		tmp = t_0;
	elseif (A <= -490000000.0)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (A <= 2.15e-78)
		tmp = t_0;
	elseif (A <= 3e-53)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((C - B) / B))) / pi;
	t_1 = (180.0 / pi) * atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -5.5e+102)
		tmp = t_1;
	elseif (A <= -1.72e+68)
		tmp = t_0;
	elseif (A <= -490000000.0)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (A <= 2.15e-78)
		tmp = t_0;
	elseif (A <= 3e-53)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.5e+102], t$95$1, If[LessEqual[A, -1.72e+68], t$95$0, If[LessEqual[A, -490000000.0], t$95$1, If[LessEqual[A, 1e-236], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.15e-78], t$95$0, If[LessEqual[A, 3e-53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -5.49999999999999981e102 or -1.72e68 < A < -4.9e8

   1. Initial program 15.8%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in B around 0 64.0%

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

      1. unpow2 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in C around 0 75.2%

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

   if -5.49999999999999981e102 < A < -1.72e68 or 1e-236 < A < 2.14999999999999997e-78

   1. Initial program 63.0%

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

      1. associate-*r/ 63.0%

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

      2. associate-*l/ 63.0%

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

      3. *-un-lft-identity 63.0%

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

      4. associate--l- 59.0%

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

      5. unpow2 59.0%

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

      6. pow2 59.0%

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

      7. hypot-def 88.0%

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

   3. Applied egg-rr 88.0%

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

   4. Taylor expanded in B around inf 65.2%

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

   if -4.9e8 < A < 1e-236

   1. Initial program 48.9%

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

   3. Simplified 48.9%

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

   4. Taylor expanded in A around 0 47.9%

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

      1. unpow2 47.9%

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

      2. unpow2 47.9%

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

      3. hypot-def 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in B around -inf 51.3%

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

   if 2.14999999999999997e-78 < A < 3.0000000000000002e-53

   1. Initial program 30.8%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in B around 0 53.9%

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

      1. unpow2 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in C around inf 77.3%

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

      1. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if 3.0000000000000002e-53 < A

   1. Initial program 84.5%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 84.5%

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

      3. *-un-lft-identity 84.5%

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

      4. associate--l- 84.5%

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

      5. unpow2 84.5%

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

      6. pow2 84.5%

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

      7. hypot-def 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in B around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

      3. distribute-neg-in 83.6%

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

      4. sub-neg 83.6%

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

      5. div-sub 83.6%

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

      6. mul-1-neg 83.6%

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

      7. associate-*r/ 83.6%

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

      8. *-inverses 83.6%

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

      9. sub-neg 83.6%

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

      10. metadata-eval 83.6%

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

      11. +-commutative 83.6%

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

      12. mul-1-neg 83.6%

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

      13. unsub-neg 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in A around 0 83.6%

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

       1. distribute-neg-in 83.6%

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

       2. metadata-eval 83.6%

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

       3. sub-neg 83.6%

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

       4. associate-*r/ 83.6%

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

       5. associate-*l/ 83.6%

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

       6. *-commutative 83.6%

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

   12. Simplified 83.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -1.72 \cdot 10^{+68}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -490000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 17: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -7 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -8 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1800000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-235}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.04 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C B) B))) PI))
        (t_1 (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))))
   (if (<= A -7e+101)
     t_1
     (if (<= A -8e+67)
       t_0
       (if (<= A -1800000000.0)
         t_1
         (if (<= A 3e-235)
           (/ (* 180.0 (atan (/ (+ B C) B))) PI)
           (if (<= A 2.4e-78)
             t_0
             (if (<= A 1.04e-53)
               (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
               (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	double t_1 = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7e+101) {
		tmp = t_1;
	} else if (A <= -8e+67) {
		tmp = t_0;
	} else if (A <= -1800000000.0) {
		tmp = t_1;
	} else if (A <= 3e-235) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 1.04e-53) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	double t_1 = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7e+101) {
		tmp = t_1;
	} else if (A <= -8e+67) {
		tmp = t_0;
	} else if (A <= -1800000000.0) {
		tmp = t_1;
	} else if (A <= 3e-235) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else if (A <= 2.4e-78) {
		tmp = t_0;
	} else if (A <= 1.04e-53) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((C - B) / B))) / math.pi
	t_1 = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -7e+101:
		tmp = t_1
	elif A <= -8e+67:
		tmp = t_0
	elif A <= -1800000000.0:
		tmp = t_1
	elif A <= 3e-235:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	elif A <= 2.4e-78:
		tmp = t_0
	elif A <= 1.04e-53:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi)
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))))
	tmp = 0.0
	if (A <= -7e+101)
		tmp = t_1;
	elseif (A <= -8e+67)
		tmp = t_0;
	elseif (A <= -1800000000.0)
		tmp = t_1;
	elseif (A <= 3e-235)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi);
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 1.04e-53)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((C - B) / B))) / pi;
	t_1 = (180.0 / pi) * atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -7e+101)
		tmp = t_1;
	elseif (A <= -8e+67)
		tmp = t_0;
	elseif (A <= -1800000000.0)
		tmp = t_1;
	elseif (A <= 3e-235)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	elseif (A <= 2.4e-78)
		tmp = t_0;
	elseif (A <= 1.04e-53)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7e+101], t$95$1, If[LessEqual[A, -8e+67], t$95$0, If[LessEqual[A, -1800000000.0], t$95$1, If[LessEqual[A, 3e-235], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.4e-78], t$95$0, If[LessEqual[A, 1.04e-53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -7.00000000000000046e101 or -7.99999999999999986e67 < A < -1.8e9

   1. Initial program 15.8%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in B around 0 64.0%

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

      1. unpow2 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in C around 0 75.2%

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

   if -7.00000000000000046e101 < A < -7.99999999999999986e67 or 2.9999999999999999e-235 < A < 2.4e-78

   1. Initial program 63.0%

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

      1. associate-*r/ 63.0%

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

      2. associate-*l/ 63.0%

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

      3. *-un-lft-identity 63.0%

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

      4. associate--l- 59.0%

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

      5. unpow2 59.0%

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

      6. pow2 59.0%

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

      7. hypot-def 88.0%

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

   3. Applied egg-rr 88.0%

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

   4. Taylor expanded in B around inf 65.2%

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

   if -1.8e9 < A < 2.9999999999999999e-235

   1. Initial program 48.9%

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

      1. associate-*r/ 49.0%

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

      2. associate-*l/ 49.0%

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

      3. *-un-lft-identity 49.0%

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

      4. associate--l- 49.0%

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

      5. unpow2 49.0%

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

      6. pow2 49.0%

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

      7. hypot-def 78.2%

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

   3. Applied egg-rr 78.2%

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

   4. Taylor expanded in B around -inf 51.4%

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

      1. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   if 2.4e-78 < A < 1.04000000000000001e-53

   1. Initial program 30.8%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in B around 0 53.9%

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

      1. unpow2 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in C around inf 77.3%

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

      1. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if 1.04000000000000001e-53 < A

   1. Initial program 84.5%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 84.5%

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

      3. *-un-lft-identity 84.5%

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

      4. associate--l- 84.5%

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

      5. unpow2 84.5%

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

      6. pow2 84.5%

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

      7. hypot-def 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in B around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

      3. distribute-neg-in 83.6%

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

      4. sub-neg 83.6%

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

      5. div-sub 83.6%

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

      6. mul-1-neg 83.6%

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

      7. associate-*r/ 83.6%

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

      8. *-inverses 83.6%

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

      9. sub-neg 83.6%

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

      10. metadata-eval 83.6%

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

      11. +-commutative 83.6%

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

      12. mul-1-neg 83.6%

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

      13. unsub-neg 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in A around 0 83.6%

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

       1. distribute-neg-in 83.6%

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

       2. metadata-eval 83.6%

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

       3. sub-neg 83.6%

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

       4. associate-*r/ 83.6%

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

       5. associate-*l/ 83.6%

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

       6. *-commutative 83.6%

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

   12. Simplified 83.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{+101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -8 \cdot 10^{+67}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1800000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-235}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.04 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 18: 60.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{if}\;A \leq -5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C B) B))) PI))
        (t_1 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))))
   (if (<= A -5e+101)
     t_1
     (if (<= A -2.4e+68)
       t_0
       (if (<= A -7e-90)
         t_1
         (if (<= A 1e-236)
           (/ (* 180.0 (atan (/ (+ B C) B))) PI)
           (if (<= A 2.1e-78)
             t_0
             (if (<= A 9.2e-53)
               (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
               (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double tmp;
	if (A <= -5e+101) {
		tmp = t_1;
	} else if (A <= -2.4e+68) {
		tmp = t_0;
	} else if (A <= -7e-90) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else if (A <= 2.1e-78) {
		tmp = t_0;
	} else if (A <= 9.2e-53) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	double tmp;
	if (A <= -5e+101) {
		tmp = t_1;
	} else if (A <= -2.4e+68) {
		tmp = t_0;
	} else if (A <= -7e-90) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else if (A <= 2.1e-78) {
		tmp = t_0;
	} else if (A <= 9.2e-53) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((C - B) / B))) / math.pi
	t_1 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	tmp = 0
	if A <= -5e+101:
		tmp = t_1
	elif A <= -2.4e+68:
		tmp = t_0
	elif A <= -7e-90:
		tmp = t_1
	elif A <= 1e-236:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	elif A <= 2.1e-78:
		tmp = t_0
	elif A <= 9.2e-53:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	tmp = 0.0
	if (A <= -5e+101)
		tmp = t_1;
	elseif (A <= -2.4e+68)
		tmp = t_0;
	elseif (A <= -7e-90)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi);
	elseif (A <= 2.1e-78)
		tmp = t_0;
	elseif (A <= 9.2e-53)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((C - B) / B))) / pi;
	t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	tmp = 0.0;
	if (A <= -5e+101)
		tmp = t_1;
	elseif (A <= -2.4e+68)
		tmp = t_0;
	elseif (A <= -7e-90)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	elseif (A <= 2.1e-78)
		tmp = t_0;
	elseif (A <= 9.2e-53)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5e+101], t$95$1, If[LessEqual[A, -2.4e+68], t$95$0, If[LessEqual[A, -7e-90], t$95$1, If[LessEqual[A, 1e-236], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.1e-78], t$95$0, If[LessEqual[A, 9.2e-53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -4.99999999999999989e101 or -2.40000000000000008e68 < A < -6.9999999999999997e-90

   1. Initial program 20.4%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in B around 0 59.7%

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

      1. unpow2 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in C around -inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 75.9%

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

      3. associate-*r/ 75.9%

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

      4. mul-1-neg 75.9%

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

      5. sub-neg 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in B around 0 75.8%

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

       1. associate-*r/ 75.8%

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

       2. associate-*l/ 75.7%

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

       3. *-commutative 75.7%

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

   12. Simplified 75.7%

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

   if -4.99999999999999989e101 < A < -2.40000000000000008e68 or 1e-236 < A < 2.1000000000000001e-78

   1. Initial program 63.0%

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

      1. associate-*r/ 63.0%

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

      2. associate-*l/ 63.0%

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

      3. *-un-lft-identity 63.0%

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

      4. associate--l- 59.0%

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

      5. unpow2 59.0%

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

      6. pow2 59.0%

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

      7. hypot-def 88.0%

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

   3. Applied egg-rr 88.0%

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

   4. Taylor expanded in B around inf 65.2%

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

   if -6.9999999999999997e-90 < A < 1e-236

   1. Initial program 52.6%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 52.6%

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

      3. *-un-lft-identity 52.6%

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

      4. associate--l- 52.6%

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

      5. unpow2 52.6%

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

      6. pow2 52.6%

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

      7. hypot-def 81.5%

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

   3. Applied egg-rr 81.5%

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

   4. Taylor expanded in B around -inf 56.2%

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

      1. mul-1-neg 56.2%

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

   6. Simplified 56.2%

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

   if 2.1000000000000001e-78 < A < 9.2000000000000005e-53

   1. Initial program 30.8%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in B around 0 53.9%

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

      1. unpow2 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in C around inf 77.3%

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

      1. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if 9.2000000000000005e-53 < A

   1. Initial program 84.5%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 84.5%

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

      3. *-un-lft-identity 84.5%

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

      4. associate--l- 84.5%

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

      5. unpow2 84.5%

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

      6. pow2 84.5%

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

      7. hypot-def 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in B around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

      3. distribute-neg-in 83.6%

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

      4. sub-neg 83.6%

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

      5. div-sub 83.6%

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

      6. mul-1-neg 83.6%

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

      7. associate-*r/ 83.6%

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

      8. *-inverses 83.6%

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

      9. sub-neg 83.6%

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

      10. metadata-eval 83.6%

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

      11. +-commutative 83.6%

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

      12. mul-1-neg 83.6%

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

      13. unsub-neg 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in A around 0 83.6%

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

       1. distribute-neg-in 83.6%

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

       2. metadata-eval 83.6%

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

       3. sub-neg 83.6%

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

       4. associate-*r/ 83.6%

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

       5. associate-*l/ 83.6%

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

       6. *-commutative 83.6%

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

   12. Simplified 83.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 19: 62.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{if}\;A \leq -5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- C B) B))) PI))
        (t_1 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))))
   (if (<= A -5e+101)
     t_1
     (if (<= A -2.4e+68)
       t_0
       (if (<= A -5e-95)
         t_1
         (if (<= A 1e-236)
           (/ (* 180.0 (atan (/ (+ B C) B))) PI)
           (if (<= A 9.6e-129)
             t_0
             (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double tmp;
	if (A <= -5e+101) {
		tmp = t_1;
	} else if (A <= -2.4e+68) {
		tmp = t_0;
	} else if (A <= -5e-95) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else if (A <= 9.6e-129) {
		tmp = t_0;
	} 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 t_0 = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	double tmp;
	if (A <= -5e+101) {
		tmp = t_1;
	} else if (A <= -2.4e+68) {
		tmp = t_0;
	} else if (A <= -5e-95) {
		tmp = t_1;
	} else if (A <= 1e-236) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else if (A <= 9.6e-129) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((C - B) / B))) / math.pi
	t_1 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	tmp = 0
	if A <= -5e+101:
		tmp = t_1
	elif A <= -2.4e+68:
		tmp = t_0
	elif A <= -5e-95:
		tmp = t_1
	elif A <= 1e-236:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	elif A <= 9.6e-129:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	tmp = 0.0
	if (A <= -5e+101)
		tmp = t_1;
	elseif (A <= -2.4e+68)
		tmp = t_0;
	elseif (A <= -5e-95)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi);
	elseif (A <= 9.6e-129)
		tmp = t_0;
	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)
	t_0 = (180.0 * atan(((C - B) / B))) / pi;
	t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	tmp = 0.0;
	if (A <= -5e+101)
		tmp = t_1;
	elseif (A <= -2.4e+68)
		tmp = t_0;
	elseif (A <= -5e-95)
		tmp = t_1;
	elseif (A <= 1e-236)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	elseif (A <= 9.6e-129)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5e+101], t$95$1, If[LessEqual[A, -2.4e+68], t$95$0, If[LessEqual[A, -5e-95], t$95$1, If[LessEqual[A, 1e-236], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 9.6e-129], t$95$0, 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 4 regimes

2. if A < -4.99999999999999989e101 or -2.40000000000000008e68 < A < -4.9999999999999998e-95

   1. Initial program 20.4%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in B around 0 59.7%

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

      1. unpow2 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in C around -inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 75.9%

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

      3. associate-*r/ 75.9%

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

      4. mul-1-neg 75.9%

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

      5. sub-neg 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in B around 0 75.8%

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

       1. associate-*r/ 75.8%

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

       2. associate-*l/ 75.7%

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

       3. *-commutative 75.7%

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

   12. Simplified 75.7%

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

   if -4.99999999999999989e101 < A < -2.40000000000000008e68 or 1e-236 < A < 9.59999999999999954e-129

   1. Initial program 60.1%

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

      1. associate-*r/ 60.1%

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

      2. associate-*l/ 60.1%

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

      3. *-un-lft-identity 60.1%

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

      4. associate--l- 55.0%

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

      5. unpow2 55.0%

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

      6. pow2 55.0%

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

      7. hypot-def 84.8%

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

   3. Applied egg-rr 84.8%

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

   4. Taylor expanded in B around inf 70.9%

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

   if -4.9999999999999998e-95 < A < 1e-236

   1. Initial program 52.6%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 52.6%

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

      3. *-un-lft-identity 52.6%

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

      4. associate--l- 52.6%

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

      5. unpow2 52.6%

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

      6. pow2 52.6%

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

      7. hypot-def 81.5%

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

   3. Applied egg-rr 81.5%

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

   4. Taylor expanded in B around -inf 56.2%

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

      1. mul-1-neg 56.2%

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

   6. Simplified 56.2%

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

   if 9.59999999999999954e-129 < A

   1. Initial program 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in B around -inf 79.8%

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

      1. associate--l+ 79.8%

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

      2. div-sub 79.8%

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

   6. Simplified 79.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-129}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20: 57.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -240000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-120} \lor \neg \left(A \leq 3.6 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -240000000.0)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 3.8e-235)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (if (or (<= A 2.8e-120) (not (<= A 3.6e-53)))
       (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -240000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 3.8e-235) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if ((A <= 2.8e-120) || !(A <= 3.6e-53)) {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -240000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 3.8e-235) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if ((A <= 2.8e-120) || !(A <= 3.6e-53)) {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -240000000.0:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 3.8e-235:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif (A <= 2.8e-120) or not (A <= 3.6e-53):
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -240000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 3.8e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif ((A <= 2.8e-120) || !(A <= 3.6e-53))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -240000000.0)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 3.8e-235)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif ((A <= 2.8e-120) || ~((A <= 3.6e-53)))
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -240000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-235], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 2.8e-120], N[Not[LessEqual[A, 3.6e-53]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.4e8

   1. Initial program 23.1%

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

   3. Simplified 36.9%

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

   4. Taylor expanded in B around 0 57.7%

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

      1. unpow2 57.7%

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

   6. Simplified 57.7%

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

   7. Taylor expanded in C around 0 67.0%

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

   if -2.4e8 < A < 3.80000000000000026e-235

   1. Initial program 48.9%

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

   3. Simplified 48.9%

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

   4. Taylor expanded in A around 0 47.9%

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

      1. unpow2 47.9%

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

      2. unpow2 47.9%

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

      3. hypot-def 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in B around -inf 51.3%

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

   if 3.80000000000000026e-235 < A < 2.79999999999999994e-120 or 3.5999999999999999e-53 < A

   1. Initial program 79.7%

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

      1. associate-*r/ 79.7%

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

      2. associate-*l/ 79.6%

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

      3. *-un-lft-identity 79.6%

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

      4. associate--l- 79.6%

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

      5. unpow2 79.6%

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

      6. pow2 79.6%

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

      7. hypot-def 96.4%

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

   3. Applied egg-rr 96.4%

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

   4. Taylor expanded in B around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in C around 0 76.4%

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

      1. associate-*r/ 76.4%

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

      2. neg-mul-1 76.4%

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

      3. distribute-neg-in 76.4%

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

      4. sub-neg 76.4%

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

      5. div-sub 76.4%

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

      6. mul-1-neg 76.4%

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

      7. associate-*r/ 76.4%

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

      8. *-inverses 76.4%

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

      9. sub-neg 76.4%

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

      10. metadata-eval 76.4%

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

      11. +-commutative 76.4%

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

      12. mul-1-neg 76.4%

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

      13. unsub-neg 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in A around 0 76.4%

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

       1. distribute-neg-in 76.4%

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

       2. metadata-eval 76.4%

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

       3. sub-neg 76.4%

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

       4. associate-*r/ 76.4%

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

       5. associate-*l/ 76.4%

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

       6. *-commutative 76.4%

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

   12. Simplified 76.4%

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

   if 2.79999999999999994e-120 < A < 3.5999999999999999e-53

   1. Initial program 49.2%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in B around 0 41.2%

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

      1. unpow2 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in C around inf 54.1%

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

      1. associate-*r/ 54.1%

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

   9. Simplified 54.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -240000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-120} \lor \neg \left(A \leq 3.6 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 21: 54.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -940000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.85 \cdot 10^{-62}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ B C) B)) PI))))
   (if (<= A -940000000.0)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A 7.8e-235)
       t_0
       (if (<= A 8.6e-130)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 3.85e-62) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	double tmp;
	if (A <= -940000000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 7.8e-235) {
		tmp = t_0;
	} else if (A <= 8.6e-130) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.85e-62) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	double tmp;
	if (A <= -940000000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 7.8e-235) {
		tmp = t_0;
	} else if (A <= 8.6e-130) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.85e-62) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	tmp = 0
	if A <= -940000000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 7.8e-235:
		tmp = t_0
	elif A <= 8.6e-130:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.85e-62:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi))
	tmp = 0.0
	if (A <= -940000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 7.8e-235)
		tmp = t_0;
	elseif (A <= 8.6e-130)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.85e-62)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B + C) / B)) / pi);
	tmp = 0.0;
	if (A <= -940000000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 7.8e-235)
		tmp = t_0;
	elseif (A <= 8.6e-130)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.85e-62)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -940000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.8e-235], t$95$0, If[LessEqual[A, 8.6e-130], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.85e-62], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -9.4e8

   1. Initial program 23.1%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in A around -inf 66.9%

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

      1. associate-*r/ 66.9%

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

   6. Simplified 66.9%

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

   if -9.4e8 < A < 7.79999999999999939e-235 or 8.60000000000000058e-130 < A < 3.84999999999999998e-62

   1. Initial program 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in A around 0 48.3%

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

      1. unpow2 48.3%

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

      2. unpow2 48.3%

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

      3. hypot-def 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in B around -inf 50.5%

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

   if 7.79999999999999939e-235 < A < 8.60000000000000058e-130

   1. Initial program 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in B around inf 54.2%

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

   if 3.84999999999999998e-62 < A

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in A around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -940000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.85 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 22: 48.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.4e-102)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 9e-236)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A 5.6e-128)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e-102) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 9e-236) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 5.6e-128) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e-102) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 9e-236) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 5.6e-128) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.4e-102:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 9e-236:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 5.6e-128:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.4e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 9e-236)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 5.6e-128)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.4e-102)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 9e-236)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 5.6e-128)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.4e-102], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e-236], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.6e-128], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -6.39999999999999973e-102

   1. Initial program 26.3%

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

   3. Simplified 22.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   if -6.39999999999999973e-102 < A < 8.99999999999999997e-236

   1. Initial program 53.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 53.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 40.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 8.99999999999999997e-236 < A < 5.5999999999999996e-128

   1. Initial program 64.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 54.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 5.5999999999999996e-128 < A

   1. Initial program 78.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around inf 66.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-2 \cdot A}{B}\right)}}{\pi} \]

      2. *-commutative 66.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]

   6. Simplified 66.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A \cdot -2}{B}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 23: 48.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7e-101)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1e-236)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A 5.8e-130)
       (* 180.0 (/ (atan -1.0) PI))
       (/ (* 180.0 (atan (/ (- A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-101) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1e-236) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 5.8e-130) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-101) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1e-236) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 5.8e-130) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7e-101:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1e-236:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 5.8e-130:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1e-236)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 5.8e-130)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7e-101)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1e-236)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 5.8e-130)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan((-A / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7e-101], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1e-236], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.8e-130], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -6.99999999999999989e-101

   1. Initial program 26.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 22.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   6. Simplified 58.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   if -6.99999999999999989e-101 < A < 1e-236

   1. Initial program 53.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 53.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 40.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 1e-236 < A < 5.8e-130

   1. Initial program 64.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 54.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 5.8e-130 < A

   1. Initial program 78.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 78.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 78.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 78.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. associate--l- 78.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]

      5. unpow2 78.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      6. pow2 78.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      7. hypot-def 93.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)}{B}\right)}{\pi} \]

   3. Applied egg-rr 93.0%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 77.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 77.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 77.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]

   7. Taylor expanded in A around inf 65.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. associate-*r/ 65.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 65.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   9. Simplified 65.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-236}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 24: 58.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -145000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -145000000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 2.6e-235)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -145000000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 2.6e-235) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -145000000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 2.6e-235) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -145000000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 2.6e-235:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -145000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 2.6e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -145000000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 2.6e-235)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -145000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e-235], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.45e8

   1. Initial program 23.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 18.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around -inf 66.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   6. Simplified 66.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   if -1.45e8 < A < 2.6e-235

   1. Initial program 48.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 48.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around 0 47.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 47.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 47.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 77.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 77.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   7. Taylor expanded in B around -inf 51.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{B + C}}{B}\right)}{\pi} \]

   if 2.6e-235 < A

   1. Initial program 75.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 75.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. associate--l- 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]

      5. unpow2 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      6. pow2 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      7. hypot-def 91.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)}{B}\right)}{\pi} \]

   3. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 76.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 76.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 76.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around 0 68.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + B}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + B\right)}{B}\right)}}{\pi} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + B\right)}}{B}\right)}{\pi} \]

      3. distribute-neg-in 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(-A\right) + \left(-B\right)}}{B}\right)}{\pi} \]

      4. sub-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(-A\right) - B}}{B}\right)}{\pi} \]

      5. div-sub 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-A}{B} - \frac{B}{B}\right)}}{\pi} \]

      6. mul-1-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-1 \cdot A}}{B} - \frac{B}{B}\right)}{\pi} \]

      7. associate-*r/ 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{-1 \cdot \frac{A}{B}} - \frac{B}{B}\right)}{\pi} \]

      8. *-inverses 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \frac{A}{B} - \color{blue}{1}\right)}{\pi} \]

      9. sub-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} + \left(-1\right)\right)}}{\pi} \]

      10. metadata-eval 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \frac{A}{B} + \color{blue}{-1}\right)}{\pi} \]

      11. +-commutative 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]

      12. mul-1-neg 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 + \color{blue}{\left(-\frac{A}{B}\right)}\right)}{\pi} \]

      13. unsub-neg 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   9. Simplified 68.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   10. Taylor expanded in A around 0 68.7%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-\left(1 + \frac{A}{B}\right)\right)}{\pi}} \]
   11. Step-by-step derivation

       1. distribute-neg-in 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1\right) + \left(-\frac{A}{B}\right)\right)}}{\pi} \]

       2. metadata-eval 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{-1} + \left(-\frac{A}{B}\right)\right)}{\pi} \]

       3. sub-neg 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

       4. associate-*r/ 68.7%

          \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}} \]

       5. associate-*l/ 68.7%

          \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)} \]

       6. *-commutative 68.7%

          \[\leadsto \color{blue}{\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}} \]

   12. Simplified 68.7%

       \[\leadsto \color{blue}{\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -145000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 25: 58.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3300000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3300000000.0)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 2.5e-235)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3300000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 2.5e-235) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3300000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 2.5e-235) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3300000000.0:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 2.5e-235:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3300000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 2.5e-235)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3300000000.0)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 2.5e-235)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3300000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.5e-235], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.3e9

   1. Initial program 23.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 36.9%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)} \]

   4. Taylor expanded in B around 0 57.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{{B}^{2}}{C - A}}}{B}\right) \]
   5. Step-by-step derivation

      1. unpow2 57.7%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{\color{blue}{B \cdot B}}{C - A}}{B}\right) \]

   6. Simplified 57.7%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{B \cdot B}{C - A}}}{B}\right) \]

   7. Taylor expanded in C around 0 67.0%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)} \]

   if -3.3e9 < A < 2.4999999999999999e-235

   1. Initial program 48.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 48.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in A around 0 47.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. unpow2 47.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 47.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-def 77.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   6. Simplified 77.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   7. Taylor expanded in B around -inf 51.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{B + C}}{B}\right)}{\pi} \]

   if 2.4999999999999999e-235 < A

   1. Initial program 75.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 75.2%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. associate--l- 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]

      5. unpow2 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      6. pow2 75.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      7. hypot-def 91.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)}{B}\right)}{\pi} \]

   3. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 76.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 76.5%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 76.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around 0 68.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + B}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + B\right)}{B}\right)}}{\pi} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-\left(A + B\right)}}{B}\right)}{\pi} \]

      3. distribute-neg-in 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(-A\right) + \left(-B\right)}}{B}\right)}{\pi} \]

      4. sub-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(-A\right) - B}}{B}\right)}{\pi} \]

      5. div-sub 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-A}{B} - \frac{B}{B}\right)}}{\pi} \]

      6. mul-1-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-1 \cdot A}}{B} - \frac{B}{B}\right)}{\pi} \]

      7. associate-*r/ 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{-1 \cdot \frac{A}{B}} - \frac{B}{B}\right)}{\pi} \]

      8. *-inverses 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \frac{A}{B} - \color{blue}{1}\right)}{\pi} \]

      9. sub-neg 68.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} + \left(-1\right)\right)}}{\pi} \]

      10. metadata-eval 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \frac{A}{B} + \color{blue}{-1}\right)}{\pi} \]

      11. +-commutative 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]

      12. mul-1-neg 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 + \color{blue}{\left(-\frac{A}{B}\right)}\right)}{\pi} \]

      13. unsub-neg 68.7%

          \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   9. Simplified 68.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   10. Taylor expanded in A around 0 68.7%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-\left(1 + \frac{A}{B}\right)\right)}{\pi}} \]
   11. Step-by-step derivation

       1. distribute-neg-in 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1\right) + \left(-\frac{A}{B}\right)\right)}}{\pi} \]

       2. metadata-eval 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{-1} + \left(-\frac{A}{B}\right)\right)}{\pi} \]

       3. sub-neg 68.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

       4. associate-*r/ 68.7%

          \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}} \]

       5. associate-*l/ 68.7%

          \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)} \]

       6. *-commutative 68.7%

          \[\leadsto \color{blue}{\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}} \]

   12. Simplified 68.7%

       \[\leadsto \color{blue}{\tan^{-1} \left(-1 - \frac{A}{B}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3300000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]

Alternative 26: 47.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -190000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-70}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -190000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5e-70)
     (/ (* 180.0 (atan (/ (- A) B))) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -190000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5e-70) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -190000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5e-70) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -190000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5e-70:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -190000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5e-70)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -190000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5e-70)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -190000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-70], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.9e5

   1. Initial program 44.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 44.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 69.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.9e5 < B < 4.9999999999999998e-70

   1. Initial program 61.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 61.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 61.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 61.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. associate--l- 58.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \left(A + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]

      5. unpow2 58.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)}{B}\right)}{\pi} \]

      6. pow2 58.6%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right)}{\pi} \]

      7. hypot-def 64.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)}{B}\right)}{\pi} \]

   3. Applied egg-rr 64.0%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 50.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 50.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 50.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]

   7. Taylor expanded in A around inf 37.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. associate-*r/ 37.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 37.2%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   9. Simplified 37.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]

   if 4.9999999999999998e-70 < B

   1. Initial program 47.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 47.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 55.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -190000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-70}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 27: 43.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6e-39)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7e-70)
     (* 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 <= -6e-39) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7e-70) {
		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 <= -6e-39) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7e-70) {
		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 <= -6e-39:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7e-70:
		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 <= -6e-39)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7e-70)
		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 <= -6e-39)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7e-70)
		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, -6e-39], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-70], 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 < -6.00000000000000055e-39

   1. Initial program 49.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 49.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 61.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -6.00000000000000055e-39 < B < 6.99999999999999949e-70

   1. Initial program 59.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 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 C around inf 26.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + -1 \cdot A}{B}\right)}}{\pi} \]

      2. distribute-rgt1-in 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-\frac{\color{blue}{\left(-1 + 1\right) \cdot A}}{B}\right)}{\pi} \]

      3. metadata-eval 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-\frac{\color{blue}{0} \cdot A}{B}\right)}{\pi} \]

      4. mul0-lft 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-\frac{\color{blue}{0}}{B}\right)}{\pi} \]

      5. distribute-frac-neg 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-0}{B}\right)}}{\pi} \]

      6. metadata-eval 26.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   6. Simplified 26.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 6.99999999999999949e-70 < B

   1. Initial program 48.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 48.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 56.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 28: 46.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.9e-33)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.7e-65)
     (/ (* 180.0 (atan (/ C B))) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.9e-33) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.7e-65) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.9e-33) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.7e-65) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.9e-33:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.7e-65:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.9e-33)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.7e-65)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.9e-33)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.7e-65)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.9e-33], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.7e-65], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.89999999999999974e-33

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 48.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 62.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -3.89999999999999974e-33 < B < 4.7000000000000001e-65

   1. Initial program 60.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*r/ 60.8%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 60.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 60.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. 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 63.8%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)}{B}\right)}{\pi} \]

   3. Applied egg-rr 63.8%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 50.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C + -1 \cdot B\right) - A}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C + \color{blue}{\left(-B\right)}\right) - A}{B}\right)}{\pi} \]

      2. unsub-neg 50.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right)} - A}{B}\right)}{\pi} \]

   6. Simplified 50.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - B\right) - A}}{B}\right)}{\pi} \]

   7. Taylor expanded in C around inf 33.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   if 4.7000000000000001e-65 < B

   1. Initial program 47.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 57.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 29: 39.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-311}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-311) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-311) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-311) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-311:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-311)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-311)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-311], 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 < -5.00000000000023e-311

   1. Initial program 51.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 50.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 43.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -5.00000000000023e-311 < B

   1. Initial program 54.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 53.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 39.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-311}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 30: 20.8% 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 53.1%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

3. Simplified 51.7%

   \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

4. Taylor expanded in B around inf 21.7%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

5. Final simplification 21.7%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023272 
(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)))