ABCF->ab-angle angle

Percentage Accurate: 53.2% → 89.0%

Time: 16.7s

Alternatives: 19

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: 53.2% 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: 89.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or 0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 60.6%

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

      1. associate-*r/ 60.6%

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

      2. associate-*l/ 60.6%

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

      3. *-commutative 60.6%

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

   3. Simplified 87.0%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 20.9%

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

      1. associate-*r/ 20.9%

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

      2. associate-*l/ 20.9%

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

      3. *-commutative 20.9%

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

   3. Simplified 20.9%

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

   4. Taylor expanded in B around 0 99.3%

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

      1. associate-*r/ 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 88.7%

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

Alternative 2: 75.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.7 \cdot 10^{+172}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.7e+172)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A 8.5e+98)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.7e+172) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= 8.5e+98) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.7e+172) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= 8.5e+98) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.7e+172:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= 8.5e+98:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.7e+172)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= 8.5e+98)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.7e+172)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= 8.5e+98)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.7e+172], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.5e+98], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.7e172

   1. Initial program 10.1%

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

      1. associate-*r/ 10.1%

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

      2. associate-*l/ 10.1%

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

      3. *-commutative 10.1%

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

   3. Simplified 42.0%

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

   4. Taylor expanded in B around 0 88.6%

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

      1. associate-*r/ 88.6%

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

   6. Simplified 88.6%

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

   if -5.7e172 < A < 8.4999999999999996e98

   1. Initial program 52.9%

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

      1. associate-*r/ 52.9%

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

      2. associate-*l/ 52.9%

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

      3. associate-*l/ 52.9%

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

      4. *-lft-identity 52.9%

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

      5. sub-neg 52.9%

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

      6. associate-+l- 51.9%

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

      7. sub-neg 51.9%

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

      8. remove-double-neg 51.9%

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

      9. +-commutative 51.9%

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

      10. unpow2 51.9%

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

      11. unpow2 51.9%

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

      12. hypot-def 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in A around 0 50.5%

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

      1. unpow2 50.5%

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

      2. unpow2 50.5%

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

      3. hypot-def 74.6%

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

   6. Simplified 74.6%

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

   if 8.4999999999999996e98 < A

   1. Initial program 86.7%

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

      1. associate-*r/ 86.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*l/ 86.7%

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

      4. *-lft-identity 86.7%

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

      5. sub-neg 86.7%

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

      6. associate-+l- 86.7%

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

      7. sub-neg 86.7%

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

      8. remove-double-neg 86.7%

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

      9. +-commutative 86.7%

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

      10. unpow2 86.7%

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

      11. unpow2 86.7%

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

      12. hypot-def 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in B around -inf 93.3%

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

      1. neg-mul-1 93.3%

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

      2. unsub-neg 93.3%

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

   6. Simplified 93.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.7 \cdot 10^{+172}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \end{array} \]

Alternative 3: 52.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} -1\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;C \leq -1.85 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq -3.6 \cdot 10^{-179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -5.4 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan -1.0)))
        (t_1 (* (/ 180.0 PI) (atan (/ (+ B C) B)))))
   (if (<= C -1.85e-105)
     t_1
     (if (<= C -3.6e-179)
       t_0
       (if (<= C -5.4e-236)
         t_1
         (if (<= C 6.2e-295)
           t_0
           (if (<= C 3.2e-109)
             (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
             (if (<= C 1.35e-68)
               t_0
               (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(-1.0);
	double t_1 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double tmp;
	if (C <= -1.85e-105) {
		tmp = t_1;
	} else if (C <= -3.6e-179) {
		tmp = t_0;
	} else if (C <= -5.4e-236) {
		tmp = t_1;
	} else if (C <= 6.2e-295) {
		tmp = t_0;
	} else if (C <= 3.2e-109) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 1.35e-68) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(-1.0);
	double t_1 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double tmp;
	if (C <= -1.85e-105) {
		tmp = t_1;
	} else if (C <= -3.6e-179) {
		tmp = t_0;
	} else if (C <= -5.4e-236) {
		tmp = t_1;
	} else if (C <= 6.2e-295) {
		tmp = t_0;
	} else if (C <= 3.2e-109) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 1.35e-68) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(-1.0)
	t_1 = (180.0 / math.pi) * math.atan(((B + C) / B))
	tmp = 0
	if C <= -1.85e-105:
		tmp = t_1
	elif C <= -3.6e-179:
		tmp = t_0
	elif C <= -5.4e-236:
		tmp = t_1
	elif C <= 6.2e-295:
		tmp = t_0
	elif C <= 3.2e-109:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 1.35e-68:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(-1.0))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)))
	tmp = 0.0
	if (C <= -1.85e-105)
		tmp = t_1;
	elseif (C <= -3.6e-179)
		tmp = t_0;
	elseif (C <= -5.4e-236)
		tmp = t_1;
	elseif (C <= 6.2e-295)
		tmp = t_0;
	elseif (C <= 3.2e-109)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 1.35e-68)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(-1.0);
	t_1 = (180.0 / pi) * atan(((B + C) / B));
	tmp = 0.0;
	if (C <= -1.85e-105)
		tmp = t_1;
	elseif (C <= -3.6e-179)
		tmp = t_0;
	elseif (C <= -5.4e-236)
		tmp = t_1;
	elseif (C <= 6.2e-295)
		tmp = t_0;
	elseif (C <= 3.2e-109)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 1.35e-68)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.85e-105], t$95$1, If[LessEqual[C, -3.6e-179], t$95$0, If[LessEqual[C, -5.4e-236], t$95$1, If[LessEqual[C, 6.2e-295], t$95$0, If[LessEqual[C, 3.2e-109], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.35e-68], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.85000000000000004e-105 or -3.60000000000000007e-179 < C < -5.4e-236

   1. Initial program 68.9%

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

      1. associate-*r/ 68.9%

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

      2. associate-*l/ 68.9%

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

      3. associate-*l/ 68.9%

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

      4. *-lft-identity 68.9%

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

      5. sub-neg 68.9%

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

      6. associate-+l- 68.9%

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

      7. sub-neg 68.9%

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

      8. remove-double-neg 68.9%

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

      9. +-commutative 68.9%

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

      10. unpow2 68.9%

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

      11. unpow2 68.9%

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

      12. hypot-def 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in A around 0 66.6%

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

      1. unpow2 66.6%

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

      2. unpow2 66.6%

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

      3. hypot-def 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in B around -inf 67.9%

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

   if -1.85000000000000004e-105 < C < -3.60000000000000007e-179 or -5.4e-236 < C < 6.2000000000000004e-295 or 3.2000000000000002e-109 < C < 1.3500000000000001e-68

   1. Initial program 64.3%

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

      1. associate-*r/ 64.3%

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

      2. associate-*l/ 64.3%

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

      3. *-commutative 64.3%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in B around inf 53.6%

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

   if 6.2000000000000004e-295 < C < 3.2000000000000002e-109

   1. Initial program 54.8%

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

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.8%

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

      3. *-commutative 54.8%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in A around -inf 37.7%

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

   if 1.3500000000000001e-68 < C

   1. Initial program 29.0%

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

      1. associate-*r/ 29.0%

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

      2. associate-*l/ 29.0%

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

      3. *-commutative 29.0%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in B around 0 71.6%

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

      1. associate-*r/ 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in C around inf 69.7%

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

      1. associate-*r/ 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-/l* 69.7%

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

   9. Simplified 69.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.85 \cdot 10^{-105}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq -3.6 \cdot 10^{-179}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq -5.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \]

Alternative 4: 59.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-137} \lor \neg \left(B \leq 1.9 \cdot 10^{+85}\right) \land B \leq 5.5 \cdot 10^{+113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.1e-72)
   (* (/ 180.0 PI) (atan (/ (+ B C) B)))
   (if (or (<= B 1.35e-137) (and (not (<= B 1.9e+85)) (<= B 5.5e+113)))
     (* 180.0 (/ (atan (/ 0.5 (/ (- A C) B))) PI))
     (* (/ 180.0 PI) (atan (/ (- C B) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e-72) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if ((B <= 1.35e-137) || (!(B <= 1.9e+85) && (B <= 5.5e+113))) {
		tmp = 180.0 * (atan((0.5 / ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.1e-72) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if ((B <= 1.35e-137) || (!(B <= 1.9e+85) && (B <= 5.5e+113))) {
		tmp = 180.0 * (Math.atan((0.5 / ((A - C) / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.1e-72:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif (B <= 1.35e-137) or (not (B <= 1.9e+85) and (B <= 5.5e+113)):
		tmp = 180.0 * (math.atan((0.5 / ((A - C) / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.1e-72)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif ((B <= 1.35e-137) || (!(B <= 1.9e+85) && (B <= 5.5e+113)))
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.1e-72)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif ((B <= 1.35e-137) || (~((B <= 1.9e+85)) && (B <= 5.5e+113)))
		tmp = 180.0 * (atan((0.5 / ((A - C) / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.1e-72], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.35e-137], And[N[Not[LessEqual[B, 1.9e+85]], $MachinePrecision], LessEqual[B, 5.5e+113]]], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.10000000000000003e-72

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. associate-*l/ 48.9%

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

      4. *-lft-identity 48.9%

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

      5. sub-neg 48.9%

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

      6. associate-+l- 48.9%

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

      7. sub-neg 48.9%

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

      8. remove-double-neg 48.9%

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

      9. +-commutative 48.9%

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

      10. unpow2 48.9%

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

      11. unpow2 48.9%

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

      12. hypot-def 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in A around 0 44.4%

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

      1. unpow2 44.4%

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

      2. unpow2 44.4%

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

      3. hypot-def 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in B around -inf 71.8%

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

   if -4.10000000000000003e-72 < B < 1.34999999999999996e-137 or 1.89999999999999996e85 < B < 5.5000000000000001e113

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in B around 0 59.0%

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

      1. associate-*r/ 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in C around -inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. mul-1-neg 58.9%

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

      3. sub-neg 58.9%

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

      4. associate-/l* 58.2%

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

   9. Simplified 58.2%

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

   if 1.34999999999999996e-137 < B < 1.89999999999999996e85 or 5.5000000000000001e113 < B

   1. Initial program 61.6%

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

      1. associate-*r/ 61.6%

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

      2. associate-*l/ 61.6%

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

      3. associate-*l/ 61.6%

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

      4. *-lft-identity 61.6%

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

      5. sub-neg 61.6%

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

      6. associate-+l- 61.6%

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

      7. sub-neg 61.6%

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

      8. remove-double-neg 61.6%

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

      9. +-commutative 61.6%

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

      10. unpow2 61.6%

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

      11. unpow2 61.6%

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

      12. hypot-def 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in A around 0 52.5%

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

      1. unpow2 52.5%

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

      2. unpow2 52.5%

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

      3. hypot-def 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in C around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-137} \lor \neg \left(B \leq 1.9 \cdot 10^{+85}\right) \land B \leq 5.5 \cdot 10^{+113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 5: 59.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-137} \lor \neg \left(B \leq 7.6 \cdot 10^{+85}\right) \land B \leq 3.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.8e-72)
   (* (/ 180.0 PI) (atan (/ (+ B C) B)))
   (if (or (<= B 4.2e-137) (and (not (<= B 7.6e+85)) (<= B 3.8e+112)))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (* (/ 180.0 PI) (atan (/ (- C B) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.8e-72) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if ((B <= 4.2e-137) || (!(B <= 7.6e+85) && (B <= 3.8e+112))) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.8e-72) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if ((B <= 4.2e-137) || (!(B <= 7.6e+85) && (B <= 3.8e+112))) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.8e-72:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif (B <= 4.2e-137) or (not (B <= 7.6e+85) and (B <= 3.8e+112)):
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.8e-72)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif ((B <= 4.2e-137) || (!(B <= 7.6e+85) && (B <= 3.8e+112)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.8e-72)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif ((B <= 4.2e-137) || (~((B <= 7.6e+85)) && (B <= 3.8e+112)))
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.8e-72], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 4.2e-137], And[N[Not[LessEqual[B, 7.6e+85]], $MachinePrecision], LessEqual[B, 3.8e+112]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.8000000000000001e-72

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. associate-*l/ 48.9%

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

      4. *-lft-identity 48.9%

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

      5. sub-neg 48.9%

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

      6. associate-+l- 48.9%

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

      7. sub-neg 48.9%

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

      8. remove-double-neg 48.9%

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

      9. +-commutative 48.9%

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

      10. unpow2 48.9%

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

      11. unpow2 48.9%

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

      12. hypot-def 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in A around 0 44.4%

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

      1. unpow2 44.4%

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

      2. unpow2 44.4%

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

      3. hypot-def 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in B around -inf 71.8%

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

   if -8.8000000000000001e-72 < B < 4.19999999999999983e-137 or 7.59999999999999984e85 < B < 3.80000000000000008e112

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in B around 0 59.0%

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

      1. associate-*r/ 59.0%

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

   6. Simplified 59.0%

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

   if 4.19999999999999983e-137 < B < 7.59999999999999984e85 or 3.80000000000000008e112 < B

   1. Initial program 61.6%

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

      1. associate-*r/ 61.6%

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

      2. associate-*l/ 61.6%

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

      3. associate-*l/ 61.6%

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

      4. *-lft-identity 61.6%

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

      5. sub-neg 61.6%

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

      6. associate-+l- 61.6%

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

      7. sub-neg 61.6%

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

      8. remove-double-neg 61.6%

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

      9. +-commutative 61.6%

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

      10. unpow2 61.6%

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

      11. unpow2 61.6%

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

      12. hypot-def 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in A around 0 52.5%

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

      1. unpow2 52.5%

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

      2. unpow2 52.5%

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

      3. hypot-def 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in C around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. unsub-neg 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-137} \lor \neg \left(B \leq 7.6 \cdot 10^{+85}\right) \land B \leq 3.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 6: 62.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-246} \lor \neg \left(B \leq 4.6 \cdot 10^{+81}\right) \land B \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.4e-72)
   (* (/ 180.0 PI) (atan (/ (+ B C) B)))
   (if (or (<= B 8.5e-246) (and (not (<= B 4.6e+81)) (<= B 5.1e+107)))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.4e-72) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if ((B <= 8.5e-246) || (!(B <= 4.6e+81) && (B <= 5.1e+107))) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.4e-72) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if ((B <= 8.5e-246) || (!(B <= 4.6e+81) && (B <= 5.1e+107))) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.4e-72:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif (B <= 8.5e-246) or (not (B <= 4.6e+81) and (B <= 5.1e+107)):
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.4e-72)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif ((B <= 8.5e-246) || (!(B <= 4.6e+81) && (B <= 5.1e+107)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.4e-72)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif ((B <= 8.5e-246) || (~((B <= 4.6e+81)) && (B <= 5.1e+107)))
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.4e-72], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 8.5e-246], And[N[Not[LessEqual[B, 4.6e+81]], $MachinePrecision], LessEqual[B, 5.1e+107]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.3999999999999999e-72

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. associate-*l/ 48.9%

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

      4. *-lft-identity 48.9%

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

      5. sub-neg 48.9%

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

      6. associate-+l- 48.9%

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

      7. sub-neg 48.9%

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

      8. remove-double-neg 48.9%

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

      9. +-commutative 48.9%

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

      10. unpow2 48.9%

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

      11. unpow2 48.9%

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

      12. hypot-def 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in A around 0 44.4%

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

      1. unpow2 44.4%

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

      2. unpow2 44.4%

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

      3. hypot-def 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in B around -inf 71.8%

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

   if -1.3999999999999999e-72 < B < 8.4999999999999998e-246 or 4.5999999999999998e81 < B < 5.1000000000000002e107

   1. Initial program 49.0%

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

      1. associate-*r/ 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%

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

      3. *-commutative 49.0%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in B around 0 64.8%

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

      1. associate-*r/ 64.9%

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

   6. Simplified 64.9%

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

   if 8.4999999999999998e-246 < B < 4.5999999999999998e81 or 5.1000000000000002e107 < B

   1. Initial program 60.9%

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

      1. associate-*r/ 60.9%

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

      2. associate-*l/ 60.9%

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

      3. associate-*l/ 60.9%

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

      4. *-lft-identity 60.9%

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

      5. sub-neg 60.9%

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

      6. associate-+l- 60.8%

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

      7. sub-neg 60.8%

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

      8. remove-double-neg 60.8%

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

      9. +-commutative 60.8%

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

      10. unpow2 60.8%

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

      11. unpow2 60.8%

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

      12. hypot-def 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in B around inf 76.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-246} \lor \neg \left(B \leq 4.6 \cdot 10^{+81}\right) \land B \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 7: 65.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-246} \lor \neg \left(B \leq 2.15 \cdot 10^{+86}\right) \land B \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.95e-196)
   (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
   (if (or (<= B 2.2e-246) (and (not (<= B 2.15e+86)) (<= B 5.1e+107)))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.95e-196) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else if ((B <= 2.2e-246) || (!(B <= 2.15e+86) && (B <= 5.1e+107))) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.95e-196) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else if ((B <= 2.2e-246) || (!(B <= 2.15e+86) && (B <= 5.1e+107))) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.95e-196:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	elif (B <= 2.2e-246) or (not (B <= 2.15e+86) and (B <= 5.1e+107)):
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.95e-196)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	elseif ((B <= 2.2e-246) || (!(B <= 2.15e+86) && (B <= 5.1e+107)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.95e-196)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	elseif ((B <= 2.2e-246) || (~((B <= 2.15e+86)) && (B <= 5.1e+107)))
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.95e-196], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 2.2e-246], And[N[Not[LessEqual[B, 2.15e+86]], $MachinePrecision], LessEqual[B, 5.1e+107]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.95000000000000008e-196

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. associate-*l/ 51.8%

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

      4. *-lft-identity 51.8%

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

      5. sub-neg 51.8%

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

      6. associate-+l- 51.7%

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

      7. sub-neg 51.7%

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

      8. remove-double-neg 51.7%

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

      9. +-commutative 51.7%

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

      10. unpow2 51.7%

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

      11. unpow2 51.7%

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

      12. hypot-def 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in B around -inf 74.2%

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

      1. neg-mul-1 74.2%

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

      2. unsub-neg 74.2%

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

   6. Simplified 74.2%

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

   if -1.95000000000000008e-196 < B < 2.19999999999999998e-246 or 2.1500000000000001e86 < B < 5.1000000000000002e107

   1. Initial program 42.2%

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

      1. associate-*r/ 42.2%

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

      2. associate-*l/ 42.2%

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

      3. *-commutative 42.2%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in B around 0 76.4%

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

      1. associate-*r/ 76.5%

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

   6. Simplified 76.5%

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

   if 2.19999999999999998e-246 < B < 2.1500000000000001e86 or 5.1000000000000002e107 < B

   1. Initial program 60.9%

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

      1. associate-*r/ 60.9%

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

      2. associate-*l/ 60.9%

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

      3. associate-*l/ 60.9%

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

      4. *-lft-identity 60.9%

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

      5. sub-neg 60.9%

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

      6. associate-+l- 60.8%

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

      7. sub-neg 60.8%

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

      8. remove-double-neg 60.8%

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

      9. +-commutative 60.8%

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

      10. unpow2 60.8%

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

      11. unpow2 60.8%

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

      12. hypot-def 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in B around inf 76.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.95 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-246} \lor \neg \left(B \leq 2.15 \cdot 10^{+86}\right) \land B \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 8: 65.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{+85} \lor \neg \left(B \leq 5.6 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.45e-196)
   (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
   (if (<= B 6.5e-246)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (if (or (<= B 1.9e+85) (not (<= B 5.6e+107)))
       (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))
       (/ (* 180.0 (atan (/ -0.5 (/ (- C A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.45e-196) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else if (B <= 6.5e-246) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if ((B <= 1.9e+85) || !(B <= 5.6e+107)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	} else {
		tmp = (180.0 * atan((-0.5 / ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.45e-196) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else if (B <= 6.5e-246) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if ((B <= 1.9e+85) || !(B <= 5.6e+107)) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	} else {
		tmp = (180.0 * Math.atan((-0.5 / ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.45e-196:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	elif B <= 6.5e-246:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif (B <= 1.9e+85) or not (B <= 5.6e+107):
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	else:
		tmp = (180.0 * math.atan((-0.5 / ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.45e-196)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	elseif (B <= 6.5e-246)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif ((B <= 1.9e+85) || !(B <= 5.6e+107))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 / Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.45e-196)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	elseif (B <= 6.5e-246)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif ((B <= 1.9e+85) || ~((B <= 5.6e+107)))
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	else
		tmp = (180.0 * atan((-0.5 / ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.45e-196], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-246], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.9e+85], N[Not[LessEqual[B, 5.6e+107]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 / N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.44999999999999994e-196

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. associate-*l/ 51.8%

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

      4. *-lft-identity 51.8%

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

      5. sub-neg 51.8%

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

      6. associate-+l- 51.7%

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

      7. sub-neg 51.7%

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

      8. remove-double-neg 51.7%

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

      9. +-commutative 51.7%

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

      10. unpow2 51.7%

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

      11. unpow2 51.7%

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

      12. hypot-def 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in B around -inf 74.2%

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

      1. neg-mul-1 74.2%

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

      2. unsub-neg 74.2%

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

   6. Simplified 74.2%

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

   if -1.44999999999999994e-196 < B < 6.50000000000000016e-246

   1. Initial program 47.7%

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

      1. associate-*r/ 47.7%

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

      2. associate-*l/ 47.7%

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

      3. *-commutative 47.7%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around 0 74.3%

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

      1. associate-*r/ 74.4%

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

   6. Simplified 74.4%

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

   if 6.50000000000000016e-246 < B < 1.89999999999999996e85 or 5.59999999999999969e107 < B

   1. Initial program 60.9%

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

      1. associate-*r/ 60.9%

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

      2. associate-*l/ 60.9%

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

      3. associate-*l/ 60.9%

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

      4. *-lft-identity 60.9%

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

      5. sub-neg 60.9%

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

      6. associate-+l- 60.8%

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

      7. sub-neg 60.8%

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

      8. remove-double-neg 60.8%

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

      9. +-commutative 60.8%

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

      10. unpow2 60.8%

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

      11. unpow2 60.8%

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

      12. hypot-def 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in B around inf 76.4%

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

   if 1.89999999999999996e85 < B < 5.59999999999999969e107

   1. Initial program 17.7%

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

      1. associate-*r/ 17.7%

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

      2. associate-*l/ 17.7%

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

      3. *-commutative 17.7%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in B around 0 85.7%

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

      1. associate-*r/ 85.7%

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

   6. Simplified 85.7%

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

      1. associate-*r/ 85.9%

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

      2. associate-/l* 85.9%

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

   8. Applied egg-rr 85.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{+85} \lor \neg \left(B \leq 5.6 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \end{array} \]

Alternative 9: 46.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))
   (if (<= B -4.5e-55)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= B 3.9e-200)
       t_0
       (if (<= B 1.25e-131)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B 6.2e-87) t_0 (* (/ 180.0 PI) (atan -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	double tmp;
	if (B <= -4.5e-55) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 3.9e-200) {
		tmp = t_0;
	} else if (B <= 1.25e-131) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= 6.2e-87) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-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) / C)) / Math.PI);
	double tmp;
	if (B <= -4.5e-55) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 3.9e-200) {
		tmp = t_0;
	} else if (B <= 1.25e-131) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= 6.2e-87) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	tmp = 0
	if B <= -4.5e-55:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 3.9e-200:
		tmp = t_0
	elif B <= 1.25e-131:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= 6.2e-87:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi))
	tmp = 0.0
	if (B <= -4.5e-55)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 3.9e-200)
		tmp = t_0;
	elseif (B <= 1.25e-131)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= 6.2e-87)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B * -0.5) / C)) / pi);
	tmp = 0.0;
	if (B <= -4.5e-55)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 3.9e-200)
		tmp = t_0;
	elseif (B <= 1.25e-131)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= 6.2e-87)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.5e-55], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.9e-200], t$95$0, If[LessEqual[B, 1.25e-131], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.2e-87], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.4999999999999997e-55

   1. Initial program 47.3%

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

      1. associate-*r/ 47.3%

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

      2. associate-*l/ 47.3%

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

      3. *-commutative 47.3%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 60.9%

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

   if -4.4999999999999997e-55 < B < 3.89999999999999999e-200 or 1.2500000000000001e-131 < B < 6.19999999999999995e-87

   1. Initial program 57.4%

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

      1. associate-*r/ 57.4%

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

      2. associate-*l/ 57.4%

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

      3. associate-*l/ 57.4%

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

      4. *-lft-identity 57.4%

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

      5. sub-neg 57.4%

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

      6. associate-+l- 54.9%

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

      7. sub-neg 54.9%

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

      8. remove-double-neg 54.9%

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

      9. +-commutative 54.9%

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

      10. unpow2 54.9%

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

      11. unpow2 54.9%

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

      12. hypot-def 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in C around inf 44.9%

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

      1. associate-*r/ 44.9%

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

      2. associate-/l* 44.2%

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

   9. Simplified 44.2%

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

   10. Taylor expanded in C around 0 44.9%

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

       1. associate-*r/ 44.9%

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

       2. *-commutative 44.9%

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

   12. Simplified 44.9%

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

   if 3.89999999999999999e-200 < B < 1.2500000000000001e-131

   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%

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

      3. *-commutative 52.6%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in A around -inf 51.2%

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

   5. Taylor expanded in B around 0 51.1%

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

   if 6.19999999999999995e-87 < B

   1. Initial program 58.6%

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

      1. associate-*r/ 58.6%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in B around inf 56.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 10: 46.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))
   (if (<= B -1.12e-54)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= B 1.85e-205)
       t_0
       (if (<= B 2e-132)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (if (<= B 7.6e-87) t_0 (* (/ 180.0 PI) (atan -1.0))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	double tmp;
	if (B <= -1.12e-54) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.85e-205) {
		tmp = t_0;
	} else if (B <= 2e-132) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= 7.6e-87) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-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) / C)) / Math.PI);
	double tmp;
	if (B <= -1.12e-54) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.85e-205) {
		tmp = t_0;
	} else if (B <= 2e-132) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= 7.6e-87) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	tmp = 0
	if B <= -1.12e-54:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.85e-205:
		tmp = t_0
	elif B <= 2e-132:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= 7.6e-87:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi))
	tmp = 0.0
	if (B <= -1.12e-54)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.85e-205)
		tmp = t_0;
	elseif (B <= 2e-132)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= 7.6e-87)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B * -0.5) / C)) / pi);
	tmp = 0.0;
	if (B <= -1.12e-54)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.85e-205)
		tmp = t_0;
	elseif (B <= 2e-132)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= 7.6e-87)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.12e-54], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-205], t$95$0, If[LessEqual[B, 2e-132], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.6e-87], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.11999999999999994e-54

   1. Initial program 47.3%

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

      1. associate-*r/ 47.3%

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

      2. associate-*l/ 47.3%

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

      3. *-commutative 47.3%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 60.9%

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

   if -1.11999999999999994e-54 < B < 1.85e-205 or 2e-132 < B < 7.6e-87

   1. Initial program 57.4%

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

      1. associate-*r/ 57.4%

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

      2. associate-*l/ 57.4%

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

      3. associate-*l/ 57.4%

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

      4. *-lft-identity 57.4%

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

      5. sub-neg 57.4%

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

      6. associate-+l- 54.9%

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

      7. sub-neg 54.9%

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

      8. remove-double-neg 54.9%

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

      9. +-commutative 54.9%

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

      10. unpow2 54.9%

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

      11. unpow2 54.9%

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

      12. hypot-def 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in C around inf 44.9%

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

      1. associate-*r/ 44.9%

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

      2. associate-/l* 44.2%

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

   9. Simplified 44.2%

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

   10. Taylor expanded in C around 0 44.9%

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

       1. associate-*r/ 44.9%

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

       2. *-commutative 44.9%

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

   12. Simplified 44.9%

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

   if 1.85e-205 < B < 2e-132

   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%

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

      3. *-commutative 52.6%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in A around -inf 51.2%

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

   if 7.6e-87 < B

   1. Initial program 58.6%

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

      1. associate-*r/ 58.6%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in B around inf 56.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.12 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 11: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-52)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 2.8e-201)
     (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))
     (if (<= B 3.6e-131)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= B 2.5e-86)
         (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
         (* (/ 180.0 PI) (atan -1.0)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-52) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 2.8e-201) {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	} else if (B <= 3.6e-131) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= 2.5e-86) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-52) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 2.8e-201) {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	} else if (B <= 3.6e-131) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= 2.5e-86) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-52:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 2.8e-201:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	elif B <= 3.6e-131:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= 2.5e-86:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-52)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 2.8e-201)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	elseif (B <= 3.6e-131)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= 2.5e-86)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-52)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 2.8e-201)
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	elseif (B <= 3.6e-131)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= 2.5e-86)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-52], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.8e-201], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-131], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-86], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.5999999999999999e-52

   1. Initial program 47.3%

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

      1. associate-*r/ 47.3%

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

      2. associate-*l/ 47.3%

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

      3. *-commutative 47.3%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 60.9%

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

   if -2.5999999999999999e-52 < B < 2.7999999999999999e-201

   1. Initial program 57.5%

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

      1. associate-*r/ 57.5%

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

      2. associate-*l/ 57.5%

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

      3. *-commutative 57.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in B around 0 54.8%

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

      1. associate-*r/ 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in C around inf 44.7%

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

      1. associate-*r/ 44.7%

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

      2. *-commutative 44.7%

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

      3. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   if 2.7999999999999999e-201 < B < 3.5999999999999999e-131

   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%

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

      3. *-commutative 52.6%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in A around -inf 51.2%

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

   if 3.5999999999999999e-131 < B < 2.4999999999999999e-86

   1. Initial program 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.7%

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

      3. associate-*l/ 56.7%

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

      4. *-lft-identity 56.7%

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

      5. sub-neg 56.7%

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

      6. associate-+l- 56.6%

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

      7. sub-neg 56.6%

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

      8. remove-double-neg 56.6%

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

      9. +-commutative 56.6%

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

      10. unpow2 56.6%

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

      11. unpow2 56.6%

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

      12. hypot-def 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in A around 0 49.2%

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

      1. unpow2 49.2%

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

      2. unpow2 49.2%

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

      3. hypot-def 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in C around inf 46.3%

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

      1. associate-*r/ 46.3%

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

      2. associate-/l* 46.1%

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

   9. Simplified 46.1%

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

   10. Taylor expanded in C around 0 46.4%

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

       1. associate-*r/ 46.4%

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

       2. *-commutative 46.4%

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

   12. Simplified 46.4%

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

   if 2.4999999999999999e-86 < B

   1. Initial program 58.6%

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

      1. associate-*r/ 58.6%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in B around inf 56.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 12: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-70)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -1e-198)
     (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))
     (if (<= B 3.7e-222)
       (* (/ 180.0 PI) (atan 0.0))
       (if (<= B 4e-108)
         (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
         (* (/ 180.0 PI) (atan -1.0)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-70) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -1e-198) {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	} else if (B <= 3.7e-222) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else if (B <= 4e-108) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-70) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -1e-198) {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	} else if (B <= 3.7e-222) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else if (B <= 4e-108) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.9e-70:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -1e-198:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	elif B <= 3.7e-222:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	elif B <= 4e-108:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.9e-70)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -1e-198)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	elseif (B <= 3.7e-222)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	elseif (B <= 4e-108)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.9e-70)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -1e-198)
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	elseif (B <= 3.7e-222)
		tmp = (180.0 / pi) * atan(0.0);
	elseif (B <= 4e-108)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e-70], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1e-198], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.7e-222], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-108], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.8999999999999999e-70

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. *-commutative 48.9%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in B around -inf 59.5%

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

   if -1.8999999999999999e-70 < B < -9.9999999999999991e-199

   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

      1. associate-*r/ 63.4%

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

      2. associate-*l/ 63.4%

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

      3. *-commutative 63.4%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in A around inf 62.3%

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

      1. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if -9.9999999999999991e-199 < B < 3.6999999999999999e-222

   1. Initial program 49.7%

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

      1. associate-*r/ 49.7%

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

      2. associate-*l/ 49.7%

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

      3. associate-*l/ 49.7%

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

      4. *-lft-identity 49.7%

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

      5. sub-neg 49.7%

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

      6. associate-+l- 45.0%

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

      7. sub-neg 45.0%

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

      8. remove-double-neg 45.0%

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

      9. +-commutative 45.0%

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

      10. unpow2 45.0%

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

      11. unpow2 45.0%

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

      12. hypot-def 68.2%

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

   3. Simplified 68.2%

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

      1. div-sub 30.3%

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

   5. Applied egg-rr 30.3%

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

   6. Taylor expanded in C around inf 34.1%

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

      1. distribute-rgt1-in 34.1%

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

      2. metadata-eval 34.1%

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

      3. mul0-lft 52.3%

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

      4. metadata-eval 52.3%

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

   8. Simplified 52.3%

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

   if 3.6999999999999999e-222 < B < 4.00000000000000016e-108

   1. Initial program 64.5%

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

      1. associate-*r/ 64.5%

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

      2. associate-*l/ 64.5%

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

      3. *-commutative 64.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in C around -inf 47.1%

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

   if 4.00000000000000016e-108 < B

   1. Initial program 57.3%

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

      1. associate-*r/ 57.3%

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

      2. associate-*l/ 57.3%

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

      3. *-commutative 57.3%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in B around inf 55.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 13: 45.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.6e-196)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 4.2e-213)
     (* (/ 180.0 PI) (atan 0.0))
     (if (<= B 7e-106)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.6e-196) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 4.2e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else if (B <= 7e-106) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.6e-196) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 4.2e-213) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else if (B <= 7e-106) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.6e-196:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 4.2e-213:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	elif B <= 7e-106:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.6e-196)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 4.2e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	elseif (B <= 7e-106)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9.6e-196)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 4.2e-213)
		tmp = (180.0 / pi) * atan(0.0);
	elseif (B <= 7e-106)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.6e-196], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-106], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.60000000000000082e-196

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in B around -inf 50.3%

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

   if -9.60000000000000082e-196 < B < 4.1999999999999997e-213

   1. Initial program 52.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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/ 52.2%

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

      3. associate-*l/ 52.2%

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

      4. *-lft-identity 52.2%

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

      5. sub-neg 52.2%

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

      6. associate-+l- 47.7%

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

      7. sub-neg 47.7%

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

      8. remove-double-neg 47.7%

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

      9. +-commutative 47.7%

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

      10. unpow2 47.7%

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

      11. unpow2 47.7%

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

      12. hypot-def 69.8%

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

   3. Simplified 69.8%

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

      1. div-sub 33.8%

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

   5. Applied egg-rr 33.8%

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

   6. Taylor expanded in C around inf 32.5%

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

      1. distribute-rgt1-in 32.5%

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

      2. metadata-eval 32.5%

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

      3. mul0-lft 49.8%

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

      4. metadata-eval 49.8%

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

   8. Simplified 49.8%

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

   if 4.1999999999999997e-213 < B < 7e-106

   1. Initial program 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-*l/ 56.5%

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

      3. *-commutative 56.5%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in A around -inf 37.9%

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

   5. Taylor expanded in B around 0 37.8%

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

   if 7e-106 < B

   1. Initial program 58.3%

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

      1. associate-*r/ 58.3%

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

      2. associate-*l/ 58.3%

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

      3. *-commutative 58.3%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in B around inf 56.4%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 14: 45.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-195}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.05e-195)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 4.8e-215)
     (* (/ 180.0 PI) (atan 0.0))
     (if (<= B 9e-105)
       (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-195) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 4.8e-215) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else if (B <= 9e-105) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-195) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 4.8e-215) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else if (B <= 9e-105) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.05e-195:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 4.8e-215:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	elif B <= 9e-105:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.05e-195)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 4.8e-215)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	elseif (B <= 9e-105)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.05e-195)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 4.8e-215)
		tmp = (180.0 / pi) * atan(0.0);
	elseif (B <= 9e-105)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.05e-195], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-215], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-105], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.05e-195

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in B around -inf 50.3%

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

   if -1.05e-195 < B < 4.8000000000000002e-215

   1. Initial program 52.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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/ 52.2%

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

      3. associate-*l/ 52.2%

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

      4. *-lft-identity 52.2%

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

      5. sub-neg 52.2%

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

      6. associate-+l- 47.7%

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

      7. sub-neg 47.7%

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

      8. remove-double-neg 47.7%

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

      9. +-commutative 47.7%

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

      10. unpow2 47.7%

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

      11. unpow2 47.7%

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

      12. hypot-def 69.8%

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

   3. Simplified 69.8%

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

      1. div-sub 33.8%

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

   5. Applied egg-rr 33.8%

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

   6. Taylor expanded in C around inf 32.5%

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

      1. distribute-rgt1-in 32.5%

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

      2. metadata-eval 32.5%

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

      3. mul0-lft 49.8%

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

      4. metadata-eval 49.8%

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

   8. Simplified 49.8%

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

   if 4.8000000000000002e-215 < B < 8.9999999999999995e-105

   1. Initial program 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-*l/ 56.5%

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

      3. *-commutative 56.5%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in B around 0 47.2%

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

      1. associate-*r/ 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in C around -inf 47.1%

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

      1. associate-*r/ 47.1%

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

      2. mul-1-neg 47.1%

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

      3. sub-neg 47.1%

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

      4. associate-/l* 47.2%

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

   9. Simplified 47.2%

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

   10. Taylor expanded in A around inf 37.9%

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

   if 8.9999999999999995e-105 < B

   1. Initial program 58.3%

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

      1. associate-*r/ 58.3%

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

      2. associate-*l/ 58.3%

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

      3. *-commutative 58.3%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in B around inf 56.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-195}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 15: 46.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.8e-53)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -7.6e-292)
     (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
     (if (<= B 3.6e-109)
       (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.8e-53) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -7.6e-292) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 3.6e-109) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.8e-53) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -7.6e-292) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 3.6e-109) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.8e-53:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -7.6e-292:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 3.6e-109:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.8e-53)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -7.6e-292)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 3.6e-109)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.8e-53)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -7.6e-292)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 3.6e-109)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.8e-53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.6e-292], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-109], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.8000000000000004e-53

   1. Initial program 47.3%

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

      1. associate-*r/ 47.3%

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

      2. associate-*l/ 47.3%

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

      3. *-commutative 47.3%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in B around -inf 60.9%

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

   if -7.8000000000000004e-53 < B < -7.60000000000000039e-292

   1. Initial program 47.8%

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

      1. associate-*r/ 47.8%

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

      2. associate-*l/ 47.8%

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

      3. associate-*l/ 47.8%

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

      4. *-lft-identity 47.8%

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

      5. sub-neg 47.8%

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

      6. associate-+l- 45.5%

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

      7. sub-neg 45.5%

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

      8. remove-double-neg 45.5%

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

      9. +-commutative 45.5%

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

      10. unpow2 45.5%

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

      11. unpow2 45.5%

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

      12. hypot-def 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in A around 0 35.3%

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

      1. unpow2 35.3%

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

      2. unpow2 35.3%

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

      3. hypot-def 54.1%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in C around inf 50.3%

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

      1. associate-*r/ 50.3%

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

      2. associate-/l* 50.3%

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

   9. Simplified 50.3%

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

   10. Taylor expanded in C around 0 50.3%

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

       1. associate-*r/ 50.3%

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

       2. *-commutative 50.3%

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

   12. Simplified 50.3%

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

   if -7.60000000000000039e-292 < B < 3.6000000000000001e-109

   1. Initial program 66.2%

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

      1. associate-*r/ 66.2%

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

      2. associate-*l/ 66.2%

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

      3. *-commutative 66.2%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in C around -inf 44.3%

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

   if 3.6000000000000001e-109 < B

   1. Initial program 57.3%

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

      1. associate-*r/ 57.3%

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

      2. associate-*l/ 57.3%

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

      3. *-commutative 57.3%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in B around inf 55.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 16: 54.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.7e-73)
   (* (/ 180.0 PI) (atan (/ (+ B C) B)))
   (if (<= B -1.35e-199)
     (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))
     (if (<= B 7.6e-222)
       (* (/ 180.0 PI) (atan 0.0))
       (* (/ 180.0 PI) (atan (/ (- C B) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-73) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (B <= -1.35e-199) {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	} else if (B <= 7.6e-222) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-73) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (B <= -1.35e-199) {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	} else if (B <= 7.6e-222) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.7e-73:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif B <= -1.35e-199:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	elif B <= 7.6e-222:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.7e-73)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (B <= -1.35e-199)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	elseif (B <= 7.6e-222)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.7e-73)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (B <= -1.35e-199)
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	elseif (B <= 7.6e-222)
		tmp = (180.0 / pi) * atan(0.0);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.7e-73], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.35e-199], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.6e-222], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.69999999999999994e-73

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. associate-*l/ 48.9%

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

      4. *-lft-identity 48.9%

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

      5. sub-neg 48.9%

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

      6. associate-+l- 48.9%

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

      7. sub-neg 48.9%

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

      8. remove-double-neg 48.9%

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

      9. +-commutative 48.9%

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

      10. unpow2 48.9%

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

      11. unpow2 48.9%

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

      12. hypot-def 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in A around 0 44.4%

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

      1. unpow2 44.4%

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

      2. unpow2 44.4%

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

      3. hypot-def 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in B around -inf 71.8%

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

   if -2.69999999999999994e-73 < B < -1.34999999999999995e-199

   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

      1. associate-*r/ 63.4%

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

      2. associate-*l/ 63.4%

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

      3. *-commutative 63.4%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in A around inf 62.3%

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

      1. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if -1.34999999999999995e-199 < B < 7.59999999999999993e-222

   1. Initial program 49.7%

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

      1. associate-*r/ 49.7%

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

      2. associate-*l/ 49.7%

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

      3. associate-*l/ 49.7%

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

      4. *-lft-identity 49.7%

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

      5. sub-neg 49.7%

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

      6. associate-+l- 45.0%

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

      7. sub-neg 45.0%

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

      8. remove-double-neg 45.0%

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

      9. +-commutative 45.0%

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

      10. unpow2 45.0%

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

      11. unpow2 45.0%

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

      12. hypot-def 68.2%

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

   3. Simplified 68.2%

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

      1. div-sub 30.3%

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

   5. Applied egg-rr 30.3%

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

   6. Taylor expanded in C around inf 34.1%

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

      1. distribute-rgt1-in 34.1%

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

      2. metadata-eval 34.1%

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

      3. mul0-lft 52.3%

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

      4. metadata-eval 52.3%

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

   8. Simplified 52.3%

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

   if 7.59999999999999993e-222 < B

   1. Initial program 58.6%

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

      1. associate-*r/ 58.6%

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

      2. associate-*l/ 58.6%

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

      3. associate-*l/ 58.6%

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

      4. *-lft-identity 58.6%

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

      5. sub-neg 58.6%

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

      6. associate-+l- 58.6%

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

      7. sub-neg 58.6%

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

      8. remove-double-neg 58.6%

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

      9. +-commutative 58.6%

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

      10. unpow2 58.6%

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

      11. unpow2 58.6%

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

      12. hypot-def 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in A around 0 49.2%

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

      1. unpow2 49.2%

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

      2. unpow2 49.2%

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

      3. hypot-def 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in C around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   9. Simplified 63.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 17: 44.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-197}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-197)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 7.6e-137)
     (* (/ 180.0 PI) (atan 0.0))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-197) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 7.6e-137) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-197) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 7.6e-137) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-197:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 7.6e-137:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-197)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 7.6e-137)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-197)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 7.6e-137)
		tmp = (180.0 / pi) * atan(0.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-197], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.6e-137], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -9.9999999999999999e-198

   1. Initial program 51.8%

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

      1. associate-*r/ 51.8%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in B around -inf 50.3%

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

   if -9.9999999999999999e-198 < B < 7.59999999999999997e-137

   1. Initial program 51.4%

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

      1. associate-*r/ 51.4%

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

      2. associate-*l/ 51.4%

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

      3. associate-*l/ 51.4%

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

      4. *-lft-identity 51.4%

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

      5. sub-neg 51.4%

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

      6. associate-+l- 47.8%

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

      7. sub-neg 47.8%

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

      8. remove-double-neg 47.8%

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

      9. +-commutative 47.8%

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

      10. unpow2 47.8%

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

      11. unpow2 47.8%

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

      12. hypot-def 64.4%

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

   3. Simplified 64.4%

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

      1. div-sub 37.2%

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

   5. Applied egg-rr 37.2%

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

   6. Taylor expanded in C around inf 25.3%

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

      1. distribute-rgt1-in 25.3%

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

      2. metadata-eval 25.3%

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

      3. mul0-lft 42.3%

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

      4. metadata-eval 42.3%

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

   8. Simplified 42.3%

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

   if 7.59999999999999997e-137 < B

   1. Initial program 59.0%

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

      1. associate-*r/ 59.0%

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

      2. associate-*l/ 59.0%

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

      3. *-commutative 59.0%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in B around inf 52.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-197}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 18: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-303)
   (* (/ 180.0 PI) (atan 1.0))
   (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-303) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-303) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.9e-303:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.9e-303)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.9e-303)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e-303], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.90000000000000005e-303

   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/ 48.9%

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

      2. associate-*l/ 48.9%

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

      3. *-commutative 48.9%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in B around -inf 43.1%

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

   if -1.90000000000000005e-303 < B

   1. Initial program 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.3%

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

      3. *-commutative 59.3%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in B around inf 42.3%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 19: 21.1% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 54.9%

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

   1. associate-*r/ 54.9%

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

   2. associate-*l/ 54.9%

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

   3. *-commutative 54.9%

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

3. Simplified 77.4%

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

4. Taylor expanded in B around inf 25.1%

   \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]

5. Final simplification 25.1%

   \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} -1 \]

Reproduce

herbie shell --seed 2023200 
(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)))