ABCF->ab-angle angle

Percentage Accurate: 55.8% → 81.5%

Time: 23.0s

Alternatives: 25

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: 55.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-52}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e-52)
   (* (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 <= -9.5e-52) {
		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 <= -9.5e-52) {
		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 <= -9.5e-52:
		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 <= -9.5e-52)
		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(Float64(C - A) - hypot(B, Float64(C - A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.5e-52)
		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, -9.5e-52], 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[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -9.50000000000000007e-52

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -9.50000000000000007e-52 < A

   1. Initial program 69.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 84.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-52}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.4e-51)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 3.6e+30)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (/ 1.0 (/ (/ PI 180.0) (atan (/ (+ A (hypot A B)) (- 0.0 B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e-51) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 3.6e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan(((A + hypot(A, B)) / (0.0 - B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e-51) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 3.6e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan(((A + Math.hypot(A, B)) / (0.0 - B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.4e-51:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 3.6e+30:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan(((A + math.hypot(A, B)) / (0.0 - B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.4e-51)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 3.6e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(A + hypot(A, B)) / Float64(0.0 - B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.4e-51)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 3.6e+30)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 1.0 / ((pi / 180.0) / atan(((A + hypot(A, B)) / (0.0 - B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.4e-51], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.6e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / N[(0.0 - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.40000000000000003e-51

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -3.40000000000000003e-51 < A < 3.6000000000000002e30

   1. Initial program 63.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.4%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(B, C\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-lowering-hypot.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(B, C\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.6%

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

   if 3.6000000000000002e30 < A

   1. Initial program 84.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 94.7%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\mathsf{PI}\left(\right)}{180 \cdot \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}}\right)\right) \]

      5. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{\mathsf{PI}\left(\right)}{180}}{\color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{\mathsf{PI}\left(\right)}{180}\right), \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI}\left(\right), 180\right), \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}}{B}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right), B\right)\right)\right)\right) \]

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in C around 0

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)}, B\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(0 - \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + B \cdot B}\right)\right)\right), B\right)\right)\right)\right) \]

      7. hypot-define N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(A, B\right)\right)\right)\right), B\right)\right)\right)\right) \]

      8. hypot-lowering-hypot.f64 90.2%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right)\right), B\right)\right)\right)\right) \]

   9. Simplified 90.2%

      \[\leadsto \frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\color{blue}{0 - \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]
   10. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + \sqrt{A \cdot A + B \cdot B}\right)\right)}{B}\right)\right)\right)\right) \]

       2. distribute-frac-neg N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(\mathsf{neg}\left(\frac{A + \sqrt{A \cdot A + B \cdot B}}{B}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{neg.f64}\left(\left(\frac{A + \sqrt{A \cdot A + B \cdot B}}{B}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(A + \sqrt{A \cdot A + B \cdot B}\right), B\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + B \cdot B}\right)\right), B\right)\right)\right)\right)\right) \]

       6. hypot-define N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(A, B\right)\right)\right), B\right)\right)\right)\right)\right) \]

       7. hypot-lowering-hypot.f64 90.2%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), B\right)\right)\right)\right)\right) \]

   11. Applied egg-rr 90.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.25 \cdot 10^{-50}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.25e-50)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 3.6e+30)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (/ (atan (/ (+ A (hypot A B)) (- 0.0 B))) (/ PI 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.25e-50) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 3.6e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.25e-50) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 3.6e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = Math.atan(((A + Math.hypot(A, B)) / (0.0 - B))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.25e-50:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 3.6e+30:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = math.atan(((A + math.hypot(A, B)) / (0.0 - B))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.25e-50)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 3.6e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(0.0 - B))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.25e-50)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 3.6e+30)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.25e-50], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.6e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / N[(0.0 - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.24999999999999981e-50

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -2.24999999999999981e-50 < A < 3.6000000000000002e30

   1. Initial program 63.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.4%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(B, C\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-lowering-hypot.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(B, C\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.6%

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

   if 3.6000000000000002e30 < A

   1. Initial program 84.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 94.7%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\mathsf{PI}\left(\right)}{180 \cdot \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}}\right)\right) \]

      5. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{\mathsf{PI}\left(\right)}{180}}{\color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{\mathsf{PI}\left(\right)}{180}\right), \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI}\left(\right), 180\right), \tan^{-1} \color{blue}{\left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}}{B}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right), B\right)\right)\right)\right) \]

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in C around 0

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)}, B\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(0 - \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + {B}^{2}}\right)\right)\right), B\right)\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + B \cdot B}\right)\right)\right), B\right)\right)\right)\right) \]

      7. hypot-define N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(A, B\right)\right)\right)\right), B\right)\right)\right)\right) \]

      8. hypot-lowering-hypot.f64 90.2%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right)\right), B\right)\right)\right)\right) \]

   9. Simplified 90.2%

      \[\leadsto \frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\color{blue}{0 - \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]
   10. Step-by-step derivation

       1. clear-num N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0 - \left(A + \sqrt{A \cdot A + B \cdot B}\right)}{B}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{0 - \left(A + \sqrt{A \cdot A + B \cdot B}\right)}{B}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

       4. frac-2neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(\left(0 - \left(A + \sqrt{A \cdot A + B \cdot B}\right)\right)\right)}{\mathsf{neg}\left(B\right)}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

       5. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(A + \sqrt{A \cdot A + B \cdot B}\right)\right)\right)\right)}{\mathsf{neg}\left(B\right)}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

       6. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{A + \sqrt{A \cdot A + B \cdot B}}{\mathsf{neg}\left(B\right)}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(A + \sqrt{A \cdot A + B \cdot B}\right), \left(\mathsf{neg}\left(B\right)\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + B \cdot B}\right)\right), \left(\mathsf{neg}\left(B\right)\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

       9. hypot-define N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(A, B\right)\right)\right), \left(\mathsf{neg}\left(B\right)\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

       10. hypot-lowering-hypot.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), \left(\mathsf{neg}\left(B\right)\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

       11. neg-sub0 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), \left(0 - B\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), \mathsf{\_.f64}\left(0, B\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), \mathsf{\_.f64}\left(0, B\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

       14. PI-lowering-PI.f64 90.2%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right), \mathsf{\_.f64}\left(0, B\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   11. Applied egg-rr 90.2%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.25 \cdot 10^{-50}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-52}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(0 - \mathsf{hypot}\left(B, A\right)\right) - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e-52)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 7.2e+30)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (/ (- (- 0.0 (hypot B A)) A) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-52) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 7.2e+30) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((0.0 - hypot(B, A)) - A) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-52) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 7.2e+30) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((0.0 - Math.hypot(B, A)) - A) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e-52:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 7.2e+30:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((((0.0 - math.hypot(B, A)) - A) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e-52)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 7.2e+30)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(0.0 - hypot(B, A)) - A) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e-52)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 7.2e+30)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan((((0.0 - hypot(B, A)) - A) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e-52], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.2e+30], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(0.0 - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.0999999999999999e-52

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -2.0999999999999999e-52 < A < 7.2000000000000004e30

   1. Initial program 63.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.4%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(B, C\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-lowering-hypot.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(B, C\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.6%

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

   if 7.2000000000000004e30 < A

   1. Initial program 84.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 94.7%

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

   5. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(0 - \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{{B}^{2} + {A}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{B \cdot B + {A}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\sqrt{B \cdot B + A \cdot A}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      8. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(B, A\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. hypot-lowering-hypot.f64 90.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(B, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 90.2%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{0 - \left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right) \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-52}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(0 - \mathsf{hypot}\left(B, A\right)\right) - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.4e-50)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 6.8e+33)
     (/ (* 180.0 (atan (/ (- C (hypot C B)) B))) PI)
     (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e-50) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 6.8e+33) {
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e-50) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 6.8e+33) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(C, B)) / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.4e-50:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 6.8e+33:
		tmp = (180.0 * math.atan(((C - math.hypot(C, B)) / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.4e-50)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 6.8e+33)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(C, B)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.4e-50)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 6.8e+33)
		tmp = (180.0 * atan(((C - hypot(C, B)) / B))) / pi;
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.4e-50], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.8e+33], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.40000000000000002e-50

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -2.40000000000000002e-50 < A < 6.7999999999999999e33

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.8%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in A around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{C}^{2} + {B}^{2}}\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + {B}^{2}}\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + B \cdot B}\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. hypot-define N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(C, B\right)\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      7. hypot-lowering-hypot.f64 78.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(C, B\right)\right), B\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 78.0%

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

   if 6.7999999999999999e33 < A

   1. Initial program 85.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 96.4%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 87.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 87.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+43}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.2e-53)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (if (<= A 9e+43)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e-53) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else if (A <= 9e+43) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e-53) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else if (A <= 9e+43) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.2e-53:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	elif A <= 9e+43:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.2e-53)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	elseif (A <= 9e+43)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.2e-53)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	elseif (A <= 9e+43)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.2e-53], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+43], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.20000000000000031e-53

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -6.20000000000000031e-53 < A < 9e43

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.8%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(B, C\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-lowering-hypot.f64 78.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(B, C\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.0%

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

   if 9e43 < A

   1. Initial program 85.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 96.4%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 87.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 87.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+43}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-138}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - \left(A + B\right)\right) + \left(A - C\right) \cdot \frac{0.5}{\frac{B}{C - A}}}{B}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.4e-138)
   (/
    1.0
    (/
     (/ PI 180.0)
     (atan (+ 1.0 (/ (* (- A C) (+ (/ 0.5 (/ B (- A C))) -1.0)) B)))))
   (if (<= B 3.8e-122)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (/
      (/ (atan (/ (+ (- C (+ A B)) (* (- A C) (/ 0.5 (/ B (- C A))))) B)) PI)
      0.005555555555555556))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.4e-138) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	} else if (B <= 3.8e-122) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - (A + B)) + ((A - C) * (0.5 / (B / (C - A))))) / B)) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.4e-138) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	} else if (B <= 3.8e-122) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - (A + B)) + ((A - C) * (0.5 / (B / (C - A))))) / B)) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.4e-138:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))))
	elif B <= 3.8e-122:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - (A + B)) + ((A - C) * (0.5 / (B / (C - A))))) / B)) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.4e-138)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(1.0 + Float64(Float64(Float64(A - C) * Float64(Float64(0.5 / Float64(B / Float64(A - C))) + -1.0)) / B)))));
	elseif (B <= 3.8e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - Float64(A + B)) + Float64(Float64(A - C) * Float64(0.5 / Float64(B / Float64(C - A))))) / B)) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.4e-138)
		tmp = 1.0 / ((pi / 180.0) / atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	elseif (B <= 3.8e-122)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = (atan((((C - (A + B)) + ((A - C) * (0.5 / (B / (C - A))))) / B)) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.4e-138], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(1.0 + N[(N[(N[(A - C), $MachinePrecision] * N[(N[(0.5 / N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-122], N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] + N[(N[(A - C), $MachinePrecision] * N[(0.5 / N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.3999999999999998e-138

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 69.8%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180 \cdot \tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)}\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{\mathsf{PI}\left(\right)}{180}}{\color{blue}{\tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{\mathsf{PI}\left(\right)}{180}\right), \color{blue}{\tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI}\left(\right), 180\right), \tan^{-1} \color{blue}{\left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \tan^{-1} \left(\color{blue}{1} - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right), B\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 69.8%

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

   if -4.3999999999999998e-138 < B < 3.8000000000000001e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 3.8000000000000001e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \color{blue}{\left(B \cdot \left(1 + \frac{1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \left(1 + \frac{1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \left(\frac{\frac{1}{2} \cdot {\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot {\left(A - C\right)}^{2}\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left({\left(A - C\right)}^{2} \cdot \frac{1}{2}\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(A - C\right) \cdot \left(A - C\right)\right) \cdot \frac{1}{2}\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(A - C\right) \cdot \left(\left(A - C\right) \cdot \frac{1}{2}\right)\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(A - C\right), \left(\left(A - C\right) \cdot \frac{1}{2}\right)\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \left(\left(A - C\right) \cdot \frac{1}{2}\right)\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{*.f64}\left(\left(A - C\right), \frac{1}{2}\right)\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \frac{1}{2}\right)\right), \left({B}^{2}\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \frac{1}{2}\right)\right), \left(B \cdot B\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. *-lowering-*.f64 63.7%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(B, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \frac{1}{2}\right)\right), \mathsf{*.f64}\left(B, B\right)\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 63.7%

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

   7. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(\frac{\left(C - \left(A + B\right)\right) + \left(C - A\right) \cdot \frac{0.5}{\frac{B}{A - C}}}{B}\right)}{\pi}}{0.005555555555555556}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-138}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - \left(A + B\right)\right) + \left(A - C\right) \cdot \frac{0.5}{\frac{B}{C - A}}}{B}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} + -1\right) + \frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-138)
   (/
    1.0
    (/
     (/ PI 180.0)
     (atan (+ 1.0 (/ (* (- A C) (+ (/ 0.5 (/ B (- A C))) -1.0)) B)))))
   (if (<= B 4.2e-122)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (*
      180.0
      (/
       (atan (+ (+ (/ C B) -1.0) (* (/ -0.5 B) (* (- A C) (/ (- A C) B)))))
       PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-138) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	} else if (B <= 4.2e-122) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-138) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	} else if (B <= 4.2e-122) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-138:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))))
	elif B <= 4.2e-122:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-138)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(1.0 + Float64(Float64(Float64(A - C) * Float64(Float64(0.5 / Float64(B / Float64(A - C))) + -1.0)) / B)))));
	elseif (B <= 4.2e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C / B) + -1.0) + Float64(Float64(-0.5 / B) * Float64(Float64(A - C) * Float64(Float64(A - C) / B))))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-138)
		tmp = 1.0 / ((pi / 180.0) / atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B))));
	elseif (B <= 4.2e-122)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-138], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(1.0 + N[(N[(N[(A - C), $MachinePrecision] * N[(N[(0.5 / N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e-122], 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[(N[ArcTan[N[(N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision] + N[(N[(-0.5 / B), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.2000000000000001e-138

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 69.8%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180 \cdot \tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)}\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{\mathsf{PI}\left(\right)}{180}}{\color{blue}{\tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{\mathsf{PI}\left(\right)}{180}\right), \color{blue}{\tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI}\left(\right), 180\right), \tan^{-1} \color{blue}{\left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \tan^{-1} \left(\color{blue}{1} - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right), \mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right), B\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 69.8%

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

   if -3.2000000000000001e-138 < B < 4.19999999999999985e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 4.19999999999999985e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}} + \frac{C}{B}\right) - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}} + \left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C - A}{B} - 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2} \cdot {\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2} \cdot {\left(A - C\right)}^{2}}{B \cdot B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. times-frac N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2}}{B} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{B}\right), \left(\frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\frac{\left(A - C\right) \cdot \left(A - C\right)}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 74.6%

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

   6. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{C}{B}\right)}, 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(A, C\right), B\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(A, C\right), B\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   8. Simplified 73.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} + -1\right) + \frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} + -1\right) + \frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.8e-138)
   (/
    (* 180.0 (atan (+ 1.0 (/ (* (- A C) (+ (/ 0.5 (/ B (- A C))) -1.0)) B))))
    PI)
   (if (<= B 4.2e-122)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (*
      180.0
      (/
       (atan (+ (+ (/ C B) -1.0) (* (/ -0.5 B) (* (- A C) (/ (- A C) B)))))
       PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-138) {
		tmp = (180.0 * atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / ((double) M_PI);
	} else if (B <= 4.2e-122) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-138) {
		tmp = (180.0 * Math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / Math.PI;
	} else if (B <= 4.2e-122) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.8e-138:
		tmp = (180.0 * math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / math.pi
	elif B <= 4.2e-122:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.8e-138)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(Float64(A - C) * Float64(Float64(0.5 / Float64(B / Float64(A - C))) + -1.0)) / B)))) / pi);
	elseif (B <= 4.2e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C / B) + -1.0) + Float64(Float64(-0.5 / B) * Float64(Float64(A - C) * Float64(Float64(A - C) / B))))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.8e-138)
		tmp = (180.0 * atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / pi;
	elseif (B <= 4.2e-122)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C / B) + -1.0) + ((-0.5 / B) * ((A - C) * ((A - C) / B))))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.8e-138], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(N[(A - C), $MachinePrecision] * N[(N[(0.5 / N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 4.2e-122], 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[(N[ArcTan[N[(N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision] + N[(N[(-0.5 / B), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.8000000000000003e-138

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 69.8%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(180 \cdot \tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   7. Applied egg-rr 69.8%

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

   if -6.8000000000000003e-138 < B < 4.19999999999999985e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 4.19999999999999985e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}} + \frac{C}{B}\right) - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}} + \left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C - A}{B} - 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2} \cdot {\left(A - C\right)}^{2}}{{B}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2} \cdot {\left(A - C\right)}^{2}}{B \cdot B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. times-frac N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \left(\frac{\frac{-1}{2}}{B} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{B}\right), \left(\frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\frac{{\left(A - C\right)}^{2}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\frac{\left(A - C\right) \cdot \left(A - C\right)}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 74.6%

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

   6. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{C}{B}\right)}, 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(A, C\right), B\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, B\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(A, C\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(A, C\right), B\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   8. Simplified 73.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} + -1\right) + \frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e-252)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 2.8e-292)
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
     (if (<= A 3.8e-213)
       (* (/ 180.0 PI) (atan (/ C B)))
       (if (<= A 1.25e+23)
         (* (/ 180.0 PI) (atan -1.0))
         (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e-252) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 2.8e-292) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (A <= 3.8e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (A <= 1.25e+23) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e-252) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 2.8e-292) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (A <= 3.8e-213) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (A <= 1.25e+23) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e-252:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 2.8e-292:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif A <= 3.8e-213:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif A <= 1.25e+23:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 2.8e-292)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (A <= 3.8e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (A <= 1.25e+23)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e-252)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 2.8e-292)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (A <= 3.8e-213)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (A <= 1.25e+23)
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e-252], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.8e-292], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e+23], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.80000000000000011e-252

   1. Initial program 35.9%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 53.1%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 53.1%

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

   if -1.80000000000000011e-252 < A < 2.8000000000000001e-292

   1. Initial program 27.0%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 66.5%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 66.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2}}{C} \cdot B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{C}\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. /-lowering-/.f64 66.4%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, C\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Applied egg-rr 66.4%

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

   if 2.8000000000000001e-292 < A < 3.8e-213

   1. Initial program 74.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 95.2%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 70.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 70.6%

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

   8. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 51.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(C, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 51.7%

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

   if 3.8e-213 < A < 1.25e23

   1. Initial program 67.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 83.3%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 36.9%

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

   if 1.25e23 < A

   1. Initial program 84.4%

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

   3. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 75.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-2 \cdot A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.2e-138)
   (/
    (* 180.0 (atan (+ 1.0 (/ (* (- A C) (+ (/ 0.5 (/ B (- A C))) -1.0)) B))))
    PI)
   (if (<= B 4.3e-122)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-138) {
		tmp = (180.0 * atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / ((double) M_PI);
	} else if (B <= 4.3e-122) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-138) {
		tmp = (180.0 * Math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / Math.PI;
	} else if (B <= 4.3e-122) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.2e-138:
		tmp = (180.0 * math.atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / math.pi
	elif B <= 4.3e-122:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.2e-138)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(Float64(A - C) * Float64(Float64(0.5 / Float64(B / Float64(A - C))) + -1.0)) / B)))) / pi);
	elseif (B <= 4.3e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.2e-138)
		tmp = (180.0 * atan((1.0 + (((A - C) * ((0.5 / (B / (A - C))) + -1.0)) / B)))) / pi;
	elseif (B <= 4.3e-122)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.2e-138], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(N[(A - C), $MachinePrecision] * N[(N[(0.5 / N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 4.3e-122], 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[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.2e-138

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(A - C\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 69.8%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(180 \cdot \tan^{-1} \left(1 - \frac{\left(A - C\right) + \frac{-1}{2} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right)}{B}\right)\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   7. Applied egg-rr 69.8%

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

   if -5.2e-138 < B < 4.30000000000000019e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 4.30000000000000019e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 72.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{\left(A - C\right) \cdot \left(\frac{0.5}{\frac{B}{A - C}} + -1\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+25)
   (/ (/ (atan (/ (* B 0.5) A)) PI) 0.005555555555555556)
   (if (<= A -7e-39)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (if (<= A 2.8e+30)
       (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)
       (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+25) {
		tmp = (atan(((B * 0.5) / A)) / ((double) M_PI)) / 0.005555555555555556;
	} else if (A <= -7e-39) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else if (A <= 2.8e+30) {
		tmp = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+25) {
		tmp = (Math.atan(((B * 0.5) / A)) / Math.PI) / 0.005555555555555556;
	} else if (A <= -7e-39) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else if (A <= 2.8e+30) {
		tmp = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.6e+25:
		tmp = (math.atan(((B * 0.5) / A)) / math.pi) / 0.005555555555555556
	elif A <= -7e-39:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	elif A <= 2.8e+30:
		tmp = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.6e+25)
		tmp = Float64(Float64(atan(Float64(Float64(B * 0.5) / A)) / pi) / 0.005555555555555556);
	elseif (A <= -7e-39)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	elseif (A <= 2.8e+30)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.6e+25)
		tmp = (atan(((B * 0.5) / A)) / pi) / 0.005555555555555556;
	elseif (A <= -7e-39)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	elseif (A <= 2.8e+30)
		tmp = (180.0 * atan(((C / B) + -1.0))) / pi;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.6e+25], N[(N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], If[LessEqual[A, -7e-39], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.8e+30], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.5999999999999996e25

   1. Initial program 23.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 52.2%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 70.2%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. div-inv N/A

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

      4. associate-/r* N/A

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

      5. *-lft-identity N/A

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

      6. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot \tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)\right), \color{blue}{\left(\frac{1}{180}\right)}\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1 \cdot \tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)}{\mathsf{PI}\left(\right)}\right), \left(\frac{\color{blue}{1}}{180}\right)\right) \]

      9. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)}{\mathsf{PI}\left(\right)}\right), \left(\frac{1}{180}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right), \mathsf{PI}\left(\right)\right), \left(\frac{\color{blue}{1}}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{1}{2}}{A}\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

      15. metadata-eval 70.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   9. Applied egg-rr 70.3%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}} \]

   if -4.5999999999999996e25 < A < -6.99999999999999999e-39

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -6.99999999999999999e-39 < A < 2.79999999999999983e30

   1. Initial program 62.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.3%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 79.3%

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

   7. Taylor expanded in B around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. --lowering--.f64 51.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 51.5%

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

   10. Taylor expanded in A around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - 1\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   11. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(1\right)\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + \frac{C}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \left(\frac{C}{B}\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       5. /-lowering-/.f64 49.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(C, B\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   12. Simplified 49.8%

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

   if 2.79999999999999983e30 < A

   1. Initial program 84.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 94.7%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in B around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. --lowering--.f64 80.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 80.8%

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

   10. Taylor expanded in C around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   11. Step-by-step derivation

       1. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 \cdot 1 + -1 \cdot \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + -1 \cdot \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 - \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(-1, \left(\frac{A}{B}\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       6. /-lowering-/.f64 79.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(A, B\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   12. Simplified 79.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+25)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -4.4e-44)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (if (<= A 1.05e+31)
       (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)
       (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+25) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -4.4e-44) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else if (A <= 1.05e+31) {
		tmp = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+25) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -4.4e-44) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else if (A <= 1.05e+31) {
		tmp = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.6e+25:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -4.4e-44:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	elif A <= 1.05e+31:
		tmp = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.6e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -4.4e-44)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	elseif (A <= 1.05e+31)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.6e+25)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -4.4e-44)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	elseif (A <= 1.05e+31)
		tmp = (180.0 * atan(((C / B) + -1.0))) / pi;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.6e+25], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -4.4e-44], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e+31], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.5999999999999996e25

   1. Initial program 23.5%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 70.2%

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

   if -4.5999999999999996e25 < A < -4.40000000000000024e-44

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -4.40000000000000024e-44 < A < 1.04999999999999989e31

   1. Initial program 62.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.3%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 79.3%

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

   7. Taylor expanded in B around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. --lowering--.f64 51.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 51.5%

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

   10. Taylor expanded in A around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - 1\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   11. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(1\right)\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + \frac{C}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \left(\frac{C}{B}\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       5. /-lowering-/.f64 49.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(C, B\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   12. Simplified 49.8%

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

   if 1.04999999999999989e31 < A

   1. Initial program 84.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 94.7%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in B around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. --lowering--.f64 80.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 80.8%

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

   10. Taylor expanded in C around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   11. Step-by-step derivation

       1. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 \cdot 1 + -1 \cdot \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + -1 \cdot \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 - \frac{A}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(-1, \left(\frac{A}{B}\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       6. /-lowering-/.f64 79.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(A, B\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   12. Simplified 79.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-44}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.8e+25)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -7e-44)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (if (<= A 3.8e+31)
       (/ (* 180.0 (atan (+ (/ C B) -1.0))) PI)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+25) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -7e-44) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else if (A <= 3.8e+31) {
		tmp = (180.0 * atan(((C / B) + -1.0))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+25) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -7e-44) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else if (A <= 3.8e+31) {
		tmp = (180.0 * Math.atan(((C / B) + -1.0))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.8e+25:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -7e-44:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	elif A <= 3.8e+31:
		tmp = (180.0 * math.atan(((C / B) + -1.0))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.8e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -7e-44)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	elseif (A <= 3.8e+31)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + -1.0))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.8e+25)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -7e-44)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	elseif (A <= 3.8e+31)
		tmp = (180.0 * atan(((C / B) + -1.0))) / pi;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.8e+25], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-44], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e+31], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.79999999999999992e25

   1. Initial program 23.5%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 70.2%

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

   if -4.79999999999999992e25 < A < -6.9999999999999995e-44

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -6.9999999999999995e-44 < A < 3.8000000000000001e31

   1. Initial program 62.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.3%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   6. Applied egg-rr 79.3%

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

   7. Taylor expanded in B around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

      6. --lowering--.f64 51.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Simplified 51.5%

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

   10. Taylor expanded in A around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - 1\right)}\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]
   11. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(1\right)\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(-1 + \frac{C}{B}\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \left(\frac{C}{B}\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

       5. /-lowering-/.f64 49.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(C, B\right)\right)\right), 180\right), \mathsf{PI.f64}\left(\right)\right) \]

   12. Simplified 49.8%

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

   if 3.8000000000000001e31 < A

   1. Initial program 84.1%

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

   3. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 76.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-44}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-2}{\frac{B}{A}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.4e+25)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -7e-39)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (if (<= A 4.5e+63)
       (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
       (/ (* 180.0 (atan (/ -2.0 (/ B A)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e+25) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -7e-39) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else if (A <= 4.5e+63) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 * atan((-2.0 / (B / A)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e+25) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -7e-39) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else if (A <= 4.5e+63) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 * Math.atan((-2.0 / (B / A)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.4e+25:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -7e-39:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	elif A <= 4.5e+63:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	else:
		tmp = (180.0 * math.atan((-2.0 / (B / A)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.4e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -7e-39)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	elseif (A <= 4.5e+63)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-2.0 / Float64(B / A)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.4e+25)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -7e-39)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	elseif (A <= 4.5e+63)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	else
		tmp = (180.0 * atan((-2.0 / (B / A)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.4e+25], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-39], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.5e+63], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-2.0 / N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.4e25

   1. Initial program 23.5%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 70.2%

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

   if -5.4e25 < A < -6.99999999999999999e-39

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -6.99999999999999999e-39 < A < 4.50000000000000017e63

   1. Initial program 62.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 49.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 49.7%

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

   8. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. /-lowering-/.f64 47.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(C, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 47.6%

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

   if 4.50000000000000017e63 < A

   1. Initial program 87.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 97.9%

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

   5. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 82.8%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\tan^{-1} \left(\frac{-2 \cdot A}{B}\right) \cdot 180\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(180 \cdot \tan^{-1} \left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \tan^{-1} \left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\left(-2 \cdot \frac{A}{B}\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\left(-2 \cdot \frac{1}{\frac{B}{A}}\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\left(\frac{-2}{\frac{B}{A}}\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(-2, \left(\frac{B}{A}\right)\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(-2, \mathsf{/.f64}\left(B, A\right)\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      11. PI-lowering-PI.f64 82.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(-2, \mathsf{/.f64}\left(B, A\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right) \]

   9. Applied egg-rr 82.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-2}{\frac{B}{A}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+25)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -9.5e-46)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (if (<= A 7.5e+62)
       (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+25) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -9.5e-46) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else if (A <= 7.5e+62) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+25) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -9.5e-46) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else if (A <= 7.5e+62) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+25:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -9.5e-46:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	elif A <= 7.5e+62:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -9.5e-46)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	elseif (A <= 7.5e+62)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+25)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -9.5e-46)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	elseif (A <= 7.5e+62)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+25], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9.5e-46], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.5e+62], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.1999999999999997e25

   1. Initial program 23.5%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 70.2%

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

   if -5.1999999999999997e25 < A < -9.49999999999999993e-46

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -9.49999999999999993e-46 < A < 7.49999999999999998e62

   1. Initial program 62.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 49.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 49.7%

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

   8. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. /-lowering-/.f64 47.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(C, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 47.6%

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

   if 7.49999999999999998e62 < A

   1. Initial program 87.5%

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

   3. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 82.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.3 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.1e+26)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -6.5e-39)
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
     (if (<= A 4.3e+68)
       (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+26) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -6.5e-39) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (A <= 4.3e+68) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+26) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -6.5e-39) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (A <= 4.3e+68) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.1e+26:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -6.5e-39:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif A <= 4.3e+68:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.1e+26)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -6.5e-39)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (A <= 4.3e+68)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.1e+26)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -6.5e-39)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (A <= 4.3e+68)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.1e+26], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -6.5e-39], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.3e+68], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.10000000000000004e26

   1. Initial program 23.5%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 70.2%

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

   if -1.10000000000000004e26 < A < -6.50000000000000027e-39

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2}}{C} \cdot B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{C}\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. /-lowering-/.f64 64.1%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, C\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Applied egg-rr 64.1%

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

   if -6.50000000000000027e-39 < A < 4.3000000000000001e68

   1. Initial program 62.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 49.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 49.7%

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

   8. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. /-lowering-/.f64 47.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(C, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 47.6%

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

   if 4.3000000000000001e68 < A

   1. Initial program 87.5%

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

   3. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 82.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.3 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.7e-16)
   (* (/ 180.0 PI) (atan (/ C B)))
   (if (<= C -1.75e-239)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= C 2.8e-83)
       (* (/ 180.0 PI) (atan -1.0))
       (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.7e-16) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (C <= -1.75e-239) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (C <= 2.8e-83) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.7e-16) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (C <= -1.75e-239) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (C <= 2.8e-83) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.7e-16:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif C <= -1.75e-239:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif C <= 2.8e-83:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.7e-16)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (C <= -1.75e-239)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (C <= 2.8e-83)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.7e-16)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (C <= -1.75e-239)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (C <= 2.8e-83)
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.7e-16], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.75e-239], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.8e-83], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.7e-16

   1. Initial program 75.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 86.8%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 69.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 69.9%

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

   8. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(C, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 62.8%

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

   if -1.7e-16 < C < -1.75000000000000003e-239

   1. Initial program 69.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.2%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 34.9%

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

   if -1.75000000000000003e-239 < C < 2.8000000000000001e-83

   1. Initial program 57.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 77.1%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 36.5%

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

   if 2.8000000000000001e-83 < C

   1. Initial program 32.0%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 62.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 62.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2}}{C} \cdot B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{C}\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, C\right), B\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Applied egg-rr 62.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 65.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.7e-138)
   (* (/ 180.0 PI) (atan (/ (- C (- A B)) B)))
   (if (<= B 6.2e-122)
     (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-138) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A - B)) / B));
	} else if (B <= 6.2e-122) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-138) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A - B)) / B));
	} else if (B <= 6.2e-122) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.7e-138:
		tmp = (180.0 / math.pi) * math.atan(((C - (A - B)) / B))
	elif B <= 6.2e-122:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.7e-138)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A - B)) / B)));
	elseif (B <= 6.2e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.7e-138)
		tmp = (180.0 / pi) * atan(((C - (A - B)) / B));
	elseif (B <= 6.2e-122)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.7e-138], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.2e-122], 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[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.69999999999999991e-138

   1. Initial program 56.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 73.8%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 68.7%

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

   8. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{\left(B + C\right) - A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\left(B + C\right) - A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\left(C + B\right) - A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C + \left(B - A\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(C, \left(B - A\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(C, \mathsf{\_.f64}\left(B, A\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 68.7%

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

   if -3.69999999999999991e-138 < B < 6.1999999999999997e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 6.1999999999999997e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 72.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 65.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + t\_0\right)\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -4.8e-138)
     (* (/ 180.0 PI) (atan (+ 1.0 t_0)))
     (if (<= B 3.1e-122)
       (* (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 <= -4.8e-138) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + t_0));
	} else if (B <= 3.1e-122) {
		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 <= -4.8e-138) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + t_0));
	} else if (B <= 3.1e-122) {
		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 <= -4.8e-138:
		tmp = (180.0 / math.pi) * math.atan((1.0 + t_0))
	elif B <= 3.1e-122:
		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 <= -4.8e-138)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + t_0)));
	elseif (B <= 3.1e-122)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -4.8e-138)
		tmp = (180.0 / pi) * atan((1.0 + t_0));
	elseif (B <= 3.1e-122)
		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, -4.8e-138], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-122], 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[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.7999999999999998e-138

   1. Initial program 56.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 73.8%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 68.7%

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

   if -4.7999999999999998e-138 < B < 3.0999999999999998e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 65.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.0%

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

   if 3.0999999999999998e-122 < B

   1. Initial program 57.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 72.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 61.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq -3.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.06e+26)
   (/ (/ (atan (/ (* B 0.5) A)) PI) 0.005555555555555556)
   (if (<= A -3.3e-39)
     (/ (atan (/ B (/ C -0.5))) (/ PI 180.0))
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.06e+26) {
		tmp = (atan(((B * 0.5) / A)) / ((double) M_PI)) / 0.005555555555555556;
	} else if (A <= -3.3e-39) {
		tmp = atan((B / (C / -0.5))) / (((double) M_PI) / 180.0);
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.06e+26) {
		tmp = (Math.atan(((B * 0.5) / A)) / Math.PI) / 0.005555555555555556;
	} else if (A <= -3.3e-39) {
		tmp = Math.atan((B / (C / -0.5))) / (Math.PI / 180.0);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.06e+26:
		tmp = (math.atan(((B * 0.5) / A)) / math.pi) / 0.005555555555555556
	elif A <= -3.3e-39:
		tmp = math.atan((B / (C / -0.5))) / (math.pi / 180.0)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.06e+26)
		tmp = Float64(Float64(atan(Float64(Float64(B * 0.5) / A)) / pi) / 0.005555555555555556);
	elseif (A <= -3.3e-39)
		tmp = Float64(atan(Float64(B / Float64(C / -0.5))) / Float64(pi / 180.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.06e+26)
		tmp = (atan(((B * 0.5) / A)) / pi) / 0.005555555555555556;
	elseif (A <= -3.3e-39)
		tmp = atan((B / (C / -0.5))) / (pi / 180.0);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.06e+26], N[(N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], If[LessEqual[A, -3.3e-39], N[(N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.05999999999999997e26

   1. Initial program 23.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 52.2%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 70.2%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. div-inv N/A

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

      4. associate-/r* N/A

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

      5. *-lft-identity N/A

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

      6. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot \tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)\right), \color{blue}{\left(\frac{1}{180}\right)}\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1 \cdot \tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)}{\mathsf{PI}\left(\right)}\right), \left(\frac{\color{blue}{1}}{180}\right)\right) \]

      9. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right)}{\mathsf{PI}\left(\right)}\right), \left(\frac{1}{180}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{1}{2}}{A}\right), \mathsf{PI}\left(\right)\right), \left(\frac{\color{blue}{1}}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{1}{2}}{A}\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{1}{2}\right), A\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

      15. metadata-eval 70.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{1}{2}\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   9. Applied egg-rr 70.3%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}} \]

   if -1.05999999999999997e26 < A < -3.29999999999999985e-39

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + \frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{1}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B}{\frac{C}{\frac{-1}{2}}}\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \left(\frac{C}{\frac{-1}{2}}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      16. PI-lowering-PI.f64 64.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(B, \mathsf{/.f64}\left(C, \frac{-1}{2}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   7. Applied egg-rr 64.2%

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

   if -3.29999999999999985e-39 < A

   1. Initial program 69.1%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 60.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq -3.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 44.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.5e-138)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 5e-122)
     (* (/ 180.0 PI) (atan (/ 0.0 B)))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-138) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 5e-122) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.0 / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-138) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 5e-122) {
		tmp = (180.0 / Math.PI) * Math.atan((0.0 / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.5e-138:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 5e-122:
		tmp = (180.0 / math.pi) * math.atan((0.0 / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.5e-138)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 5e-122)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.0 / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.5e-138)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 5e-122)
		tmp = (180.0 / pi) * atan((0.0 / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.5e-138], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-122], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.0 / 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 < -6.4999999999999999e-138

   1. Initial program 56.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 73.8%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 45.0%

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

   if -6.4999999999999999e-138 < B < 4.9999999999999999e-122

   1. Initial program 51.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.3%

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

   5. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(\left(A + -1 \cdot A\right)\right)}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(\left(-1 + 1\right) \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(0 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{0}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. /-lowering-/.f64 40.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(0, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 40.5%

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

   if 4.9999999999999999e-122 < B

   1. Initial program 57.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 76.5%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 53.5%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 64.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.7e-58)
   (* (atan (* B (/ 0.5 (- A C)))) (/ 180.0 PI))
   (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.7e-58) {
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.7e-58) {
		tmp = Math.atan((B * (0.5 / (A - C)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.7e-58:
		tmp = math.atan((B * (0.5 / (A - C)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.7e-58)
		tmp = Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.7e-58)
		tmp = atan((B * (0.5 / (A - C)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.7e-58], 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[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.70000000000000032e-58

   1. Initial program 24.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 54.0%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 80.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 80.5%

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

   if -5.70000000000000032e-58 < A

   1. Initial program 69.6%

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

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 61.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 40.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.2e-307)
   (* (/ 180.0 PI) (atan 1.0))
   (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-307) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-307) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.2e-307:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.2e-307)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.2e-307)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.2e-307], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.20000000000000009e-307

   1. Initial program 54.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 73.5%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 36.6%

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

   if -1.20000000000000009e-307 < B

   1. Initial program 56.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 77.0%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 42.9%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 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 55.2%

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

   3. associate-/l* N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

3. Simplified 75.1%

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

5. Taylor expanded in B around inf

   \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
6. Step-by-step derivation

7. Simplified 20.3%

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

8. Final simplification 20.3%

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

Reproduce

herbie shell --seed 2024164 
(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)))