ABCF->ab-angle angle

Percentage Accurate: 55.5% → 82.1%

Time: 17.0s

Alternatives: 20

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e+103)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+103) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+103) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+103:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+103)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+103)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e+103], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.15000000000000004e103

   1. Initial program 16.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 21.9%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 84.1

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

   7. Simplified 84.1%

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

   if -1.15000000000000004e103 < A

   1. Initial program 66.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 83.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+93}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 380000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e+93)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 380000000.0)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+93) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 380000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+93) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 380000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+93:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 380000000.0:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+93)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 380000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e+93)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 380000000.0)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+93], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 380000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.10000000000000019e93

   1. Initial program 17.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 24.6%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

   if -3.10000000000000019e93 < A < 3.8e8

   1. Initial program 60.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 79.3%

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

   5. Taylor expanded in A around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. unpow2 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-hypot.f64 75.8

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

   7. Simplified 75.8%

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

   if 3.8e8 < A

   1. Initial program 80.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 85.4

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

   5. Simplified 85.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+93}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 380000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+104)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B A))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+104) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, A))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+104) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, A))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5e+104:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, A))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5e+104)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5e+104)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, A))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+104], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.49999999999999984e104

   1. Initial program 16.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 21.9%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 84.1

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

   7. Simplified 84.1%

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

   if -1.49999999999999984e104 < A

   1. Initial program 66.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 83.6%

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

   5. Taylor expanded in C around 0

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

      1. +-lowering-+.f64 N/A

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

      2. +-commutative N/A

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

      3. unpow2 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-hypot.f64 79.8

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

   7. Simplified 79.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq 9.8 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-175}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \left(t\_0 \cdot t\_0\right) + \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B 9.8e-224)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
     (if (<= B 4.3e-175)
       (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
       (/
        180.0
        (/
         PI
         (atan (+ (* -0.5 (* t_0 t_0)) (+ (/ C B) (- -1.0 (/ A B)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= 9.8e-224) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 4.3e-175) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((-0.5 * (t_0 * t_0)) + ((C / B) + (-1.0 - (A / B))))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= 9.8e-224) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 4.3e-175) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((-0.5 * (t_0 * t_0)) + ((C / B) + (-1.0 - (A / B))))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= 9.8e-224:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 4.3e-175:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((-0.5 * (t_0 * t_0)) + ((C / B) + (-1.0 - (A / B))))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= 9.8e-224)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 4.3e-175)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-0.5 * Float64(t_0 * t_0)) + Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= 9.8e-224)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 4.3e-175)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 / (pi / atan(((-0.5 * (t_0 * t_0)) + ((C / B) + (-1.0 - (A / B))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 9.8e-224], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.3e-175], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(-0.5 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 9.7999999999999992e-224

   1. Initial program 63.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 73.1

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

   5. Simplified 73.1%

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

   if 9.7999999999999992e-224 < B < 4.29999999999999998e-175

   1. Initial program 31.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 31.2%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 78.8

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

   7. Simplified 78.8%

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

   if 4.29999999999999998e-175 < B

   1. Initial program 51.7%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. PI-lowering-PI.f64 N/A

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

      6. atan-lowering-atan.f64 N/A

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

      7. *-commutative N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 70.3%

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

   5. Taylor expanded in B around inf

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

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

   7. Simplified 67.8%

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

Alternative 5: 47.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.65e+49)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -6.5e-199)
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
     (if (<= B 1.45e-307)
       (/ (* 180.0 (atan 0.0)) PI)
       (if (<= B 7e-51)
         (* (/ 180.0 PI) (atan (/ C B)))
         (* (/ 180.0 PI) (atan -1.0)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.65e+49) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -6.5e-199) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 1.45e-307) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 7e-51) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / 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 <= -1.65e+49) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -6.5e-199) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 1.45e-307) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 7e-51) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.65e+49:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -6.5e-199:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 1.45e-307:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 7e-51:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.65e+49)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -6.5e-199)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 1.45e-307)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 7e-51)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / 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 <= -1.65e+49)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -6.5e-199)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 1.45e-307)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 7e-51)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.65e+49], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.5e-199], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-307], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7e-51], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / 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 < -1.6499999999999999e49

   1. Initial program 54.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.6%

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

   5. Taylor expanded in B around -inf

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

   7. Simplified 74.9%

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

   if -1.6499999999999999e49 < B < -6.50000000000000017e-199

   1. Initial program 70.8%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 44.1

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

   5. Simplified 44.1%

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

   if -6.50000000000000017e-199 < B < 1.45e-307

   1. Initial program 49.8%

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 49.5%

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. --lowering--.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. accelerator-lowering-hypot.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. /-lowering-/.f64 35.0

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

   6. Applied egg-rr 35.0%

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

   7. Taylor expanded in C around inf

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. metadata-eval 49.9

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

   9. Simplified 49.9%

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

   if 1.45e-307 < B < 6.9999999999999995e-51

   1. Initial program 61.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 63.7%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 58.7

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

   7. Simplified 58.7%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 43.5

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

   10. Simplified 43.5%

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

   if 6.9999999999999995e-51 < B

   1. Initial program 48.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 71.4%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 53.4%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.5e+49)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -3.9e-148)
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
     (if (<= B 4.2e-53)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e+49) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -3.9e-148) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 4.2e-53) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} 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 <= -1.5e+49) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -3.9e-148) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 4.2e-53) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.5e+49:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -3.9e-148:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 4.2e-53:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.5e+49)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -3.9e-148)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 4.2e-53)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	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 <= -1.5e+49)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -3.9e-148)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 4.2e-53)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.5e+49], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.9e-148], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e-53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $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 < -1.5000000000000001e49

   1. Initial program 54.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.6%

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

   5. Taylor expanded in B around -inf

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

   7. Simplified 74.9%

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

   if -1.5000000000000001e49 < B < -3.89999999999999994e-148

   1. Initial program 75.2%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 44.8

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

   5. Simplified 44.8%

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

   if -3.89999999999999994e-148 < B < 4.19999999999999955e-53

   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. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 58.3%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 47.6

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

   7. Simplified 47.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 47.7

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

   9. Applied egg-rr 47.7%

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

   if 4.19999999999999955e-53 < B

   1. Initial program 49.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 71.8%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 52.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e+49)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -1.3e-148)
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
     (if (<= B 8.5e-54)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e+49) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -1.3e-148) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else if (B <= 8.5e-54) {
		tmp = 180.0 * (atan(((B * 0.5) / 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 <= -1.9e+49) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -1.3e-148) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else if (B <= 8.5e-54) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / 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 <= -1.9e+49:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -1.3e-148:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	elif B <= 8.5e-54:
		tmp = 180.0 * (math.atan(((B * 0.5) / 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 <= -1.9e+49)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -1.3e-148)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	elseif (B <= 8.5e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / 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 <= -1.9e+49)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -1.3e-148)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	elseif (B <= 8.5e-54)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e+49], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.3e-148], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-54], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $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 < -1.8999999999999999e49

   1. Initial program 54.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.6%

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

   5. Taylor expanded in B around -inf

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

   7. Simplified 74.9%

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

   if -1.8999999999999999e49 < B < -1.30000000000000004e-148

   1. Initial program 75.2%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 44.8

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

   5. Simplified 44.8%

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

   if -1.30000000000000004e-148 < B < 8.5e-54

   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. Add Preprocessing

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 47.6

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

   5. Simplified 47.6%

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

   if 8.5e-54 < B

   1. Initial program 49.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 71.8%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 52.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.7 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-306}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.7e-224)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1e-306)
       (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
       (/ (* 180.0 (atan (+ t_0 -1.0))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.7e-224) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1e-306) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_0 + -1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.7e-224) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1e-306) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((t_0 + -1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.7e-224:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1e-306:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((t_0 + -1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.7e-224)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1e-306)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + -1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.7e-224)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1e-306)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (180.0 * atan((t_0 + -1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.7e-224], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e-306], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.69999999999999996e-224

   1. Initial program 62.5%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 77.0

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

   5. Simplified 77.0%

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

   if -1.69999999999999996e-224 < B < 1.00000000000000003e-306

   1. Initial program 38.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 37.9%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 79.2

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

   7. Simplified 79.2%

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

   if 1.00000000000000003e-306 < B

   1. Initial program 54.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 68.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 64.4

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

   7. Simplified 64.4%

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

   8. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. atan-lowering-atan.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. div-sub N/A

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

      10. metadata-eval N/A

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

      11. +-lowering-+.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 N/A

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

      14. PI-lowering-PI.f64 64.4

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

   10. Simplified 64.4%

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

Alternative 9: 67.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -5.6 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-307}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -5.6e-225)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.3e-307)
       (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
       (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.6e-225) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.3e-307) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.6e-225) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.3e-307) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -5.6e-225:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.3e-307:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -5.6e-225)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.3e-307)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -5.6e-225)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.3e-307)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -5.6e-225], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-307], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.6e-225

   1. Initial program 62.5%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 77.0

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

   5. Simplified 77.0%

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

   if -5.6e-225 < B < 1.29999999999999998e-307

   1. Initial program 38.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 37.9%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 79.2

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

   7. Simplified 79.2%

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

   if 1.29999999999999998e-307 < B

   1. Initial program 54.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 68.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 64.4

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

   7. Simplified 64.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-307}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.2 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-36}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.2e-224)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 2.5e-36)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.2e-224) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 2.5e-36) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.2e-224) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 2.5e-36) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 2.2e-224:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 2.5e-36:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 2.2e-224)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 2.5e-36)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 2.2e-224)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 2.5e-36)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 2.2e-224], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-36], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 2.2000000000000001e-224

   1. Initial program 63.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 73.1

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

   5. Simplified 73.1%

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

   if 2.2000000000000001e-224 < B < 2.50000000000000002e-36

   1. Initial program 48.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 50.9%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 57.7

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

   7. Simplified 57.7%

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

   if 2.50000000000000002e-36 < B

   1. Initial program 49.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 73.8%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 70.8

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

   7. Simplified 70.8%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 66.4

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

   10. Simplified 66.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2.2 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-36}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4e+26)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 1.45e-45)
     (/ 180.0 (/ PI (atan (/ (- C B) B))))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+26) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 1.45e-45) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+26) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 1.45e-45) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4e+26:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 1.45e-45:
		tmp = 180.0 / (math.pi / math.atan(((C - B) / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4e+26)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 1.45e-45)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4e+26)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 1.45e-45)
		tmp = 180.0 / (pi / atan(((C - B) / B)));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4e+26], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.45e-45], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.00000000000000019e26

   1. Initial program 25.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 32.1%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 70.6

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

   7. Simplified 70.6%

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

   if -4.00000000000000019e26 < A < 1.45e-45

   1. Initial program 60.8%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. PI-lowering-PI.f64 N/A

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

      6. atan-lowering-atan.f64 N/A

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

      7. *-commutative N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 80.9%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 50.2%

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

   if 1.45e-45 < A

   1. Initial program 77.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 92.6%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 75.3

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

   7. Simplified 75.3%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 74.3

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

   10. Simplified 74.3%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.4e+26)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 4.2e-45)
     (* (/ 180.0 PI) (atan (/ (- C B) B)))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.4e+26) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 4.2e-45) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.4e+26) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 4.2e-45) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.4e+26:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 4.2e-45:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.4e+26)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 4.2e-45)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.4e+26)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 4.2e-45)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.4e+26], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.2e-45], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.4e26

   1. Initial program 25.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 32.1%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 70.6

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

   7. Simplified 70.6%

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

   if -1.4e26 < A < 4.1999999999999999e-45

   1. Initial program 60.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 80.9%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 50.2%

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

   if 4.1999999999999999e-45 < A

   1. Initial program 77.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 92.6%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 75.3

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

   7. Simplified 75.3%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 74.3

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

   10. Simplified 74.3%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.52 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e-231)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 1.52e-235)
     (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-231) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 1.52e-235) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-231) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 1.52e-235) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.5e-231:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 1.52e-235:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.5e-231)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 1.52e-235)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.5e-231)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 1.52e-235)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e-231], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.52e-235], 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[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.50000000000000012e-231

   1. Initial program 39.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 52.3%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 51.3

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

   7. Simplified 51.3%

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

   if -2.50000000000000012e-231 < A < 1.52e-235

   1. Initial program 67.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.0%

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

   5. Taylor expanded in C around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 48.2

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

   7. Simplified 48.2%

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

   if 1.52e-235 < A

   1. Initial program 72.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 89.9%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 70.5

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

   7. Simplified 70.5%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 67.4

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

   10. Simplified 67.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.52 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-232}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e-232)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 2.15e-235)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-232) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 2.15e-235) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-232) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 2.15e-235) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9e-232:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 2.15e-235:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9e-232)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 2.15e-235)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9e-232)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 2.15e-235)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9e-232], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.15e-235], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.99999999999999933e-232

   1. Initial program 39.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 52.3%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 51.3

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

   7. Simplified 51.3%

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

   if -8.99999999999999933e-232 < A < 2.15000000000000012e-235

   1. Initial program 67.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.0%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 63.1

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

   7. Simplified 63.1%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 48.2

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

   10. Simplified 48.2%

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

   if 2.15000000000000012e-235 < A

   1. Initial program 72.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 89.9%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 70.5

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

   7. Simplified 70.5%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 67.4

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

   10. Simplified 67.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-232}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7e-233)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (if (<= A 5.5e-235)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-233) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (A <= 5.5e-235) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-233) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (A <= 5.5e-235) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7e-233:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif A <= 5.5e-235:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7e-233)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (A <= 5.5e-235)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7e-233)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (A <= 5.5e-235)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7e-233], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.5e-235], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.99999999999999982e-233

   1. Initial program 39.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 52.3%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 51.3

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

   7. Simplified 51.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 51.3

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

   9. Applied egg-rr 51.3%

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

   if -6.99999999999999982e-233 < A < 5.4999999999999998e-235

   1. Initial program 67.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 88.0%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 63.1

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

   7. Simplified 63.1%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 48.2

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

   10. Simplified 48.2%

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

   if 5.4999999999999998e-235 < A

   1. Initial program 72.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 89.9%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 70.5

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

   7. Simplified 70.5%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 67.4

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

   10. Simplified 67.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{-235}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.5e-6)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 8.8e-48)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e-6) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 8.8e-48) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / 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 <= -7.5e-6) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 8.8e-48) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.5e-6:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 8.8e-48:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.5e-6)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 8.8e-48)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / 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 <= -7.5e-6)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 8.8e-48)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.5e-6], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.8e-48], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.50000000000000019e-6

   1. Initial program 58.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 87.7%

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

   5. Taylor expanded in B around -inf

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

   7. Simplified 68.3%

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

   if -7.50000000000000019e-6 < B < 8.8000000000000005e-48

   1. Initial program 61.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 63.1%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 53.5

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

   7. Simplified 53.5%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 37.9

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

   10. Simplified 37.9%

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

   if 8.8000000000000005e-48 < B

   1. Initial program 48.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

   3. Simplified 71.4%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 53.4%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 8.5e-47)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.5e-47) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.5e-47) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 8.5e-47:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 8.5e-47)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 8.5e-47)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 8.5e-47], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 8.4999999999999999e-47

   1. Initial program 60.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      5. --lowering--.f64 66.5

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \frac{\color{blue}{C - A}}{B}\right)}{\pi} \]

   5. Simplified 66.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if 8.4999999999999999e-47 < B

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \tan^{-1} \left(\frac{C}{B} - \color{blue}{\left(\frac{A}{B} + 1\right)}\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      2. associate--r+ N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      3. div-sub N/A

         \[\leadsto \tan^{-1} \left(\color{blue}{\frac{C - A}{B}} - 1\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      4. sub-neg N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(\frac{C - A}{B} + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval N/A

         \[\leadsto \tan^{-1} \left(\frac{C - A}{B} + \color{blue}{-1}\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(\frac{C - A}{B} + -1\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \tan^{-1} \left(\color{blue}{\frac{C - A}{B}} + -1\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      8. --lowering--.f64 68.4

         \[\leadsto \tan^{-1} \left(\frac{\color{blue}{C - A}}{B} + -1\right) \cdot \frac{180}{\pi} \]

   7. Simplified 68.4%

      \[\leadsto \tan^{-1} \color{blue}{\left(\frac{C - A}{B} + -1\right)} \cdot \frac{180}{\pi} \]

   8. Taylor expanded in C around 0

      \[\leadsto \tan^{-1} \color{blue}{\left(-1 \cdot \left(1 + \frac{A}{B}\right)\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(-1 \cdot 1 + -1 \cdot \frac{A}{B}\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      2. metadata-eval N/A

         \[\leadsto \tan^{-1} \left(\color{blue}{-1} + -1 \cdot \frac{A}{B}\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \tan^{-1} \left(-1 + \color{blue}{\left(\mathsf{neg}\left(\frac{A}{B}\right)\right)}\right) \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      4. unsub-neg N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      5. --lowering--.f64 N/A

         \[\leadsto \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]

      6. /-lowering-/.f64 64.3

         \[\leadsto \tan^{-1} \left(-1 - \color{blue}{\frac{A}{B}}\right) \cdot \frac{180}{\pi} \]

   10. Simplified 64.3%

       \[\leadsto \tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.06 \cdot 10^{-92}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.5e-58)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 1.06e-92)
     (/ (* 180.0 (atan 0.0)) PI)
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.5e-58) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.06e-92) {
		tmp = (180.0 * atan(0.0)) / ((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 <= -4.5e-58) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.06e-92) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.5e-58:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.06e-92:
		tmp = (180.0 * math.atan(0.0)) / 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 <= -4.5e-58)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.06e-92)
		tmp = Float64(Float64(180.0 * atan(0.0)) / 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 <= -4.5e-58)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.06e-92)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.5e-58], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.06e-92], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.5000000000000003e-58

   1. Initial program 61.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   6. Step-by-step derivation

   7. Simplified 61.7%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -4.5000000000000003e-58 < B < 1.06e-92

   1. Initial program 58.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)}} \]

   4. Applied egg-rr 60.2%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)} + A\right)}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      2. associate--r+ N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - \sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right) - A}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      3. div-sub N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}{B} - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      4. --lowering--.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}{B} - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\color{blue}{\frac{C - \sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}{B}} - \frac{A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{C - \sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}{B} - \frac{A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      7. accelerator-lowering-hypot.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B} - \frac{A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      8. --lowering--.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, \color{blue}{A - C}\right)}{B} - \frac{A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      9. /-lowering-/.f64 52.0

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, A - C\right)}{B} - \color{blue}{\frac{A}{B}}\right)}{\pi} \]

   6. Applied egg-rr 52.0%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, A - C\right)}{B} - \frac{A}{B}\right)}}{\pi} \]

   7. Taylor expanded in C around inf

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{A}{B} + \frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]
   8. Step-by-step derivation

      1. distribute-lft1-in N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot \frac{A}{B}\right)}\right)}{\mathsf{PI}\left(\right)} \]

      2. metadata-eval N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \left(\color{blue}{0} \cdot \frac{A}{B}\right)\right)}{\mathsf{PI}\left(\right)} \]

      3. mul0-lft N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      4. metadata-eval 32.3

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   9. Simplified 32.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{0}}{\pi} \]

   if 1.06e-92 < B

   1. Initial program 51.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   6. Step-by-step derivation

   7. Simplified 49.7%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.06 \cdot 10^{-92}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.2e-300)
   (* (/ 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 <= -4.2e-300) {
		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 <= -4.2e-300) {
		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 <= -4.2e-300:
		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 <= -4.2e-300)
		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 <= -4.2e-300)
		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, -4.2e-300], 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 < -4.20000000000000007e-300

   1. Initial program 60.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   6. Step-by-step derivation

   7. Simplified 45.0%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -4.20000000000000007e-300 < B

   1. Initial program 54.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
   6. Step-by-step derivation

   7. Simplified 37.1%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.6% accurate, 4.0× 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 57.0%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot 180} \]

   2. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\mathsf{PI}\left(\right)}} \]

   3. associate-/l* N/A

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\mathsf{PI}\left(\right)}} \]

3. Simplified 72.2%

   \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
4. Add Preprocessing

5. Taylor expanded in B around inf

   \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\mathsf{PI}\left(\right)} \]
6. Step-by-step derivation

7. Simplified 19.6%

   \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]

8. Final simplification 19.6%

   \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} -1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024192 
(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)))