ABCF->ab-angle angle

Percentage Accurate: 53.9% → 88.3%

Time: 29.2s

Alternatives: 22

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-5} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2 + A \cdot 2}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -5e-5) (not (<= t_0 0.0)))
     (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))
     (* 180.0 (/ (atan (/ B (+ (* C -2.0) (* A 2.0)))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-5) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	} else {
		tmp = 180.0 * (atan((B / ((C * -2.0) + (A * 2.0)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-5) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	} else {
		tmp = 180.0 * (Math.atan((B / ((C * -2.0) + (A * 2.0)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -5e-5) or not (t_0 <= 0.0):
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	else:
		tmp = 180.0 * (math.atan((B / ((C * -2.0) + (A * 2.0)))) / math.pi)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -5e-5) || ~((t_0 <= 0.0)))
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	else
		tmp = 180.0 * (atan((B / ((C * -2.0) + (A * 2.0)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B / N[(N[(C * -2.0), $MachinePrecision] + N[(A * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -5.00000000000000024e-5 or -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 60.0%

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

   4. Applied egg-rr 87.8%

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

   if -5.00000000000000024e-5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

   1. Initial program 23.4%

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

      1. +-commutative 23.4%

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

      2. unpow2 23.4%

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

      3. unpow2 23.4%

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

      4. hypot-udef 23.4%

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

      5. associate--r+ 8.9%

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

      6. associate-/r/ 8.9%

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

      7. associate--r+ 23.4%

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

      8. hypot-udef 23.4%

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

      9. unpow2 23.4%

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

      10. unpow2 23.4%

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

      11. +-commutative 23.4%

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

      12. unpow2 23.4%

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

      13. unpow2 23.4%

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

      14. hypot-def 23.4%

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

   4. Applied egg-rr 23.4%

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

   5. Taylor expanded in A around -inf 96.1%

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

   6. Taylor expanded in B around 0 99.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-5} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2 + A \cdot 2}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+125)
   (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
   (if (<= A 1.5e+57)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+125) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= 1.5e+57) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+125) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= 1.5e+57) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+125:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= 1.5e+57:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+125)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= 1.5e+57)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+125)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= 1.5e+57)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+125], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.5e+57], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.8000000000000002e125

   1. Initial program 15.7%

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

   4. Applied egg-rr 49.2%

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

   5. Taylor expanded in A around -inf 86.4%

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

      1. associate-*r/ 86.4%

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

   7. Simplified 86.4%

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

      1. associate-/r/ 86.5%

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

      2. associate-/l* 86.5%

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

   9. Applied egg-rr 86.5%

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

   if -1.8000000000000002e125 < A < 1.5e57

   1. Initial program 55.6%

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

   4. Applied egg-rr 80.3%

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

   5. Taylor expanded in A around 0 52.6%

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

      1. unpow2 52.6%

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

      2. unpow2 52.6%

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

      3. hypot-def 77.2%

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

   7. Simplified 77.2%

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

   if 1.5e57 < A

   1. Initial program 80.9%

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

   3. Taylor expanded in C around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. mul-1-neg 80.9%

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

      3. +-commutative 80.9%

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

      4. unpow2 80.9%

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

      5. unpow2 80.9%

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

      6. hypot-def 90.7%

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

   5. Simplified 90.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.8e+131)
   (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
   (if (<= A 9e+59)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e+131) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= 9e+59) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e+131) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= 9e+59) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.8e+131:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= 9e+59:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.8e+131)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= 9e+59)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.8e+131)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= 9e+59)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.8e+131], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e+59], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.8000000000000001e131

   1. Initial program 15.7%

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

   4. Applied egg-rr 49.2%

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

   5. Taylor expanded in A around -inf 86.4%

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

      1. associate-*r/ 86.4%

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

   7. Simplified 86.4%

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

      1. associate-/r/ 86.5%

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

      2. associate-/l* 86.5%

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

   9. Applied egg-rr 86.5%

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

   if -2.8000000000000001e131 < A < 8.99999999999999919e59

   1. Initial program 55.6%

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

   3. Taylor expanded in A around 0 52.6%

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

      1. unpow2 52.6%

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

      2. unpow2 52.6%

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

      3. hypot-def 77.2%

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

   5. Simplified 77.2%

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

   if 8.99999999999999919e59 < A

   1. Initial program 80.9%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in B around -inf 83.8%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 9 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+115}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+60}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1e+115)
   (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
   (if (<= A 7e+60)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e+115) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= 7e+60) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e+115) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= 7e+60) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1e+115:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= 7e+60:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1e+115)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= 7e+60)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1e+115)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= 7e+60)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1e+115], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7e+60], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1e115

   1. Initial program 15.7%

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

   4. Applied egg-rr 49.2%

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

   5. Taylor expanded in A around -inf 86.4%

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

      1. associate-*r/ 86.4%

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

   7. Simplified 86.4%

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

      1. associate-/r/ 86.5%

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

      2. associate-/l* 86.5%

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

   9. Applied egg-rr 86.5%

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

   if -1e115 < A < 7.0000000000000004e60

   1. Initial program 55.6%

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

   4. Applied egg-rr 80.3%

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

   5. Taylor expanded in A around 0 52.6%

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

      1. unpow2 52.6%

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

      2. unpow2 52.6%

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

      3. hypot-def 77.2%

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

   7. Simplified 77.2%

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

   if 7.0000000000000004e60 < A

   1. Initial program 80.9%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in B around -inf 83.8%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+115}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+60}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.3e+115)
   (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e+115) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e+115) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.3e+115:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.3e+115)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.3e+115)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.3e+115], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.30000000000000004e115

   1. Initial program 15.7%

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

   4. Applied egg-rr 49.2%

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

   5. Taylor expanded in A around -inf 86.4%

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

      1. associate-*r/ 86.4%

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

   7. Simplified 86.4%

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

      1. associate-/r/ 86.5%

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

      2. associate-/l* 86.5%

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

   9. Applied egg-rr 86.5%

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

   if -2.30000000000000004e115 < A

   1. Initial program 62.0%

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

   3. Simplified 83.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.6 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-243}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -5.6e-51)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.5e-198)
       t_0
       (if (<= B 1.12e-243)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 1.15e-161)
           t_0
           (if (<= B 1.25e-145)
             (* 180.0 (/ (atan (/ B A)) PI))
             (if (<= B 1.6e+15)
               (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -5.6e-51) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.5e-198) {
		tmp = t_0;
	} else if (B <= 1.12e-243) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.15e-161) {
		tmp = t_0;
	} else if (B <= 1.25e-145) {
		tmp = 180.0 * (atan((B / A)) / ((double) M_PI));
	} else if (B <= 1.6e+15) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -5.6e-51) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.5e-198) {
		tmp = t_0;
	} else if (B <= 1.12e-243) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.15e-161) {
		tmp = t_0;
	} else if (B <= 1.25e-145) {
		tmp = 180.0 * (Math.atan((B / A)) / Math.PI);
	} else if (B <= 1.6e+15) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -5.6e-51:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.5e-198:
		tmp = t_0
	elif B <= 1.12e-243:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.15e-161:
		tmp = t_0
	elif B <= 1.25e-145:
		tmp = 180.0 * (math.atan((B / A)) / math.pi)
	elif B <= 1.6e+15:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -5.6e-51)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.5e-198)
		tmp = t_0;
	elseif (B <= 1.12e-243)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.15e-161)
		tmp = t_0;
	elseif (B <= 1.25e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(B / A)) / pi));
	elseif (B <= 1.6e+15)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -5.6e-51)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.5e-198)
		tmp = t_0;
	elseif (B <= 1.12e-243)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.15e-161)
		tmp = t_0;
	elseif (B <= 1.25e-145)
		tmp = 180.0 * (atan((B / A)) / pi);
	elseif (B <= 1.6e+15)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.6e-51], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.5e-198], t$95$0, If[LessEqual[B, 1.12e-243], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-161], t$95$0, If[LessEqual[B, 1.25e-145], N[(180.0 * N[(N[ArcTan[N[(B / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e+15], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -5.6e-51

   1. Initial program 46.1%

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

   3. Taylor expanded in B around -inf 51.8%

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

   if -5.6e-51 < B < -8.4999999999999994e-198 or 1.12000000000000005e-243 < B < 1.15e-161

   1. Initial program 66.9%

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

      1. associate--l- 66.7%

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

      2. add-cube-cbrt 66.6%

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

      3. +-commutative 66.6%

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

      4. unpow2 66.6%

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

      5. unpow2 66.6%

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

      6. hypot-udef 68.5%

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

      7. fma-neg 66.6%

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

      8. *-un-lft-identity 66.6%

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

      9. *-commutative 66.6%

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

      10. pow2 66.6%

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

      11. *-commutative 66.6%

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

      12. *-un-lft-identity 66.6%

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

      13. hypot-udef 66.6%

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

      14. unpow2 66.6%

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

      15. unpow2 66.6%

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

      16. +-commutative 66.6%

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

      17. unpow2 66.6%

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

      18. unpow2 66.6%

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

   4. Applied egg-rr 66.6%

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

   5. Taylor expanded in C around -inf 56.6%

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

   if -8.4999999999999994e-198 < B < 1.12000000000000005e-243

   1. Initial program 51.4%

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

   3. Taylor expanded in C around inf 51.5%

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

      1. associate-*r/ 51.5%

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

      2. distribute-rgt1-in 51.5%

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

      3. metadata-eval 51.5%

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

      4. mul0-lft 51.5%

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

      5. metadata-eval 51.5%

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

   5. Simplified 51.5%

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

   if 1.15e-161 < B < 1.2499999999999999e-145

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. unpow2 34.9%

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

      3. unpow2 34.9%

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

      4. hypot-udef 99.5%

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

      5. associate--r+ 35.6%

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

      6. associate-/r/ 35.6%

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

      7. associate--r+ 99.5%

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

      8. hypot-udef 34.9%

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

      9. unpow2 34.9%

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

      10. unpow2 34.9%

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

      11. +-commutative 34.9%

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

      12. unpow2 34.9%

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

      13. unpow2 34.9%

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

      14. hypot-def 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in B around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in A around inf 72.9%

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

   if 1.2499999999999999e-145 < B < 1.6e15

   1. Initial program 65.1%

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

   3. Taylor expanded in A around inf 40.3%

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

   if 1.6e15 < B

   1. Initial program 52.0%

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

   3. Taylor expanded in B around inf 68.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-243}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -6e-51)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.5e-198)
       t_0
       (if (<= B 1.5e-238)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 3.1e-162)
           t_0
           (if (<= B 1.3e-145)
             (* 180.0 (/ (atan (/ B A)) PI))
             (if (<= B 1.05e+15)
               (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -6e-51) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.5e-198) {
		tmp = t_0;
	} else if (B <= 1.5e-238) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.1e-162) {
		tmp = t_0;
	} else if (B <= 1.3e-145) {
		tmp = 180.0 * (atan((B / A)) / ((double) M_PI));
	} else if (B <= 1.05e+15) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -6e-51) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.5e-198) {
		tmp = t_0;
	} else if (B <= 1.5e-238) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.1e-162) {
		tmp = t_0;
	} else if (B <= 1.3e-145) {
		tmp = 180.0 * (Math.atan((B / A)) / Math.PI);
	} else if (B <= 1.05e+15) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -6e-51:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.5e-198:
		tmp = t_0
	elif B <= 1.5e-238:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.1e-162:
		tmp = t_0
	elif B <= 1.3e-145:
		tmp = 180.0 * (math.atan((B / A)) / math.pi)
	elif B <= 1.05e+15:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -6e-51)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.5e-198)
		tmp = t_0;
	elseif (B <= 1.5e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.1e-162)
		tmp = t_0;
	elseif (B <= 1.3e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(B / A)) / pi));
	elseif (B <= 1.05e+15)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -6e-51)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.5e-198)
		tmp = t_0;
	elseif (B <= 1.5e-238)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.1e-162)
		tmp = t_0;
	elseif (B <= 1.3e-145)
		tmp = 180.0 * (atan((B / A)) / pi);
	elseif (B <= 1.05e+15)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6e-51], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.5e-198], t$95$0, If[LessEqual[B, 1.5e-238], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-162], t$95$0, If[LessEqual[B, 1.3e-145], N[(180.0 * N[(N[ArcTan[N[(B / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.05e+15], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -6.00000000000000005e-51

   1. Initial program 46.1%

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

   3. Taylor expanded in B around -inf 51.8%

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

   if -6.00000000000000005e-51 < B < -8.4999999999999994e-198 or 1.5e-238 < B < 3.0999999999999999e-162

   1. Initial program 66.9%

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

   3. Taylor expanded in C around -inf 56.7%

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

   if -8.4999999999999994e-198 < B < 1.5e-238

   1. Initial program 51.4%

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

   3. Taylor expanded in C around inf 51.5%

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

      1. associate-*r/ 51.5%

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

      2. distribute-rgt1-in 51.5%

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

      3. metadata-eval 51.5%

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

      4. mul0-lft 51.5%

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

      5. metadata-eval 51.5%

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

   5. Simplified 51.5%

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

   if 3.0999999999999999e-162 < B < 1.3e-145

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. unpow2 34.9%

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

      3. unpow2 34.9%

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

      4. hypot-udef 99.5%

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

      5. associate--r+ 35.6%

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

      6. associate-/r/ 35.6%

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

      7. associate--r+ 99.5%

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

      8. hypot-udef 34.9%

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

      9. unpow2 34.9%

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

      10. unpow2 34.9%

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

      11. +-commutative 34.9%

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

      12. unpow2 34.9%

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

      13. unpow2 34.9%

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

      14. hypot-def 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in B around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in A around inf 72.9%

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

   if 1.3e-145 < B < 1.05e15

   1. Initial program 65.1%

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

   3. Taylor expanded in A around inf 40.3%

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

   if 1.05e15 < B

   1. Initial program 52.0%

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

   3. Taylor expanded in B around inf 68.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;C \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -2.95 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= C -3.5e+39)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -1e-30)
       t_0
       (if (<= C -2.95e-120)
         (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
         (if (<= C -1.9e-253)
           t_0
           (if (<= C 5.6e-202)
             (* 180.0 (/ (atan 1.0) PI))
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (C <= -3.5e+39) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -1e-30) {
		tmp = t_0;
	} else if (C <= -2.95e-120) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (C <= -1.9e-253) {
		tmp = t_0;
	} else if (C <= 5.6e-202) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (C <= -3.5e+39) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -1e-30) {
		tmp = t_0;
	} else if (C <= -2.95e-120) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (C <= -1.9e-253) {
		tmp = t_0;
	} else if (C <= 5.6e-202) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if C <= -3.5e+39:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -1e-30:
		tmp = t_0
	elif C <= -2.95e-120:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif C <= -1.9e-253:
		tmp = t_0
	elif C <= 5.6e-202:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (C <= -3.5e+39)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -1e-30)
		tmp = t_0;
	elseif (C <= -2.95e-120)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (C <= -1.9e-253)
		tmp = t_0;
	elseif (C <= 5.6e-202)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (C <= -3.5e+39)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -1e-30)
		tmp = t_0;
	elseif (C <= -2.95e-120)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (C <= -1.9e-253)
		tmp = t_0;
	elseif (C <= 5.6e-202)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -3.5e+39], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1e-30], t$95$0, If[LessEqual[C, -2.95e-120], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.9e-253], t$95$0, If[LessEqual[C, 5.6e-202], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -3.5000000000000002e39

   1. Initial program 82.1%

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

   3. Taylor expanded in C around -inf 79.1%

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

   if -3.5000000000000002e39 < C < -1e-30 or -2.94999999999999989e-120 < C < -1.90000000000000006e-253

   1. Initial program 61.7%

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

   3. Taylor expanded in B around inf 43.7%

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

   if -1e-30 < C < -2.94999999999999989e-120

   1. Initial program 72.5%

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

   3. Taylor expanded in A around inf 42.8%

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

   if -1.90000000000000006e-253 < C < 5.6000000000000002e-202

   1. Initial program 59.5%

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

   3. Taylor expanded in B around -inf 47.8%

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

   if 5.6000000000000002e-202 < C

   1. Initial program 32.4%

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

      1. +-commutative 32.4%

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

      2. unpow2 32.4%

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

      3. unpow2 32.4%

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

      4. hypot-udef 63.7%

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

      5. associate--r+ 56.3%

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

      6. associate-/r/ 56.3%

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

      7. associate--r+ 63.7%

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

      8. hypot-udef 32.4%

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

      9. unpow2 32.4%

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

      10. unpow2 32.4%

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

      11. +-commutative 32.4%

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

      12. unpow2 32.4%

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

      13. unpow2 32.4%

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

      14. hypot-def 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in A around 0 23.0%

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

      1. unpow2 23.0%

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

      2. unpow2 23.0%

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

      3. hypot-def 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in B around 0 56.9%

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

      1. *-commutative 56.9%

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

   10. Simplified 56.9%

       \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq -2.95 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -9.5 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.7 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -9.5e-160)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C -2.4e-226)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= C -4.7e-253)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= C 1.4e-195)
         (* 180.0 (/ (atan 1.0) PI))
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.5e-160) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= -2.4e-226) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (C <= -4.7e-253) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 1.4e-195) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.5e-160) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= -2.4e-226) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (C <= -4.7e-253) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 1.4e-195) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -9.5e-160:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= -2.4e-226:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif C <= -4.7e-253:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 1.4e-195:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -9.5e-160)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= -2.4e-226)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (C <= -4.7e-253)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 1.4e-195)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -9.5e-160)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= -2.4e-226)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (C <= -4.7e-253)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 1.4e-195)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -9.5e-160], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.4e-226], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -4.7e-253], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.4e-195], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -9.5000000000000002e-160

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. unpow2 72.3%

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

      3. unpow2 72.3%

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

      4. hypot-udef 89.8%

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

      5. associate--r+ 88.1%

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

      6. associate-/r/ 88.1%

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

      7. associate--r+ 89.8%

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

      8. hypot-udef 72.3%

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

      9. unpow2 72.3%

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

      10. unpow2 72.3%

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

      11. +-commutative 72.3%

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

      12. unpow2 72.3%

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

      13. unpow2 72.3%

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

      14. hypot-def 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in A around 0 68.3%

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

      1. unpow2 68.3%

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

      2. unpow2 68.3%

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

      3. hypot-def 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in B around inf 73.3%

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

   if -9.5000000000000002e-160 < C < -2.4e-226

   1. Initial program 100.0%

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

   3. Taylor expanded in A around inf 84.1%

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

   if -2.4e-226 < C < -4.69999999999999981e-253

   1. Initial program 83.8%

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

   3. Taylor expanded in B around inf 64.4%

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

   if -4.69999999999999981e-253 < C < 1.40000000000000002e-195

   1. Initial program 59.5%

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

   3. Taylor expanded in B around -inf 47.8%

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

   if 1.40000000000000002e-195 < C

   1. Initial program 32.4%

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

      1. +-commutative 32.4%

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

      2. unpow2 32.4%

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

      3. unpow2 32.4%

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

      4. hypot-udef 63.7%

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

      5. associate--r+ 56.3%

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

      6. associate-/r/ 56.3%

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

      7. associate--r+ 63.7%

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

      8. hypot-udef 32.4%

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

      9. unpow2 32.4%

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

      10. unpow2 32.4%

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

      11. +-commutative 32.4%

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

      12. unpow2 32.4%

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

      13. unpow2 32.4%

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

      14. hypot-def 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in A around 0 23.0%

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

      1. unpow2 23.0%

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

      2. unpow2 23.0%

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

      3. hypot-def 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in B around 0 56.9%

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

      1. *-commutative 56.9%

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

   10. Simplified 56.9%

       \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -9.5 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -4.7 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.86:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))
   (if (<= A -3.6e+70)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A 4.6e-78)
       t_0
       (if (<= A 9e-56)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= A 0.86) t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double tmp;
	if (A <= -3.6e+70) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 4.6e-78) {
		tmp = t_0;
	} else if (A <= 9e-56) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (A <= 0.86) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double tmp;
	if (A <= -3.6e+70) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 4.6e-78) {
		tmp = t_0;
	} else if (A <= 9e-56) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (A <= 0.86) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	tmp = 0
	if A <= -3.6e+70:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 4.6e-78:
		tmp = t_0
	elif A <= 9e-56:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif A <= 0.86:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	tmp = 0.0
	if (A <= -3.6e+70)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 4.6e-78)
		tmp = t_0;
	elseif (A <= 9e-56)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (A <= 0.86)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	tmp = 0.0;
	if (A <= -3.6e+70)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 4.6e-78)
		tmp = t_0;
	elseif (A <= 9e-56)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (A <= 0.86)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.6e+70], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.6e-78], t$95$0, If[LessEqual[A, 9e-56], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 0.86], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -3.6e70

   1. Initial program 20.6%

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

   3. Taylor expanded in A around -inf 75.6%

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

      1. associate-*r/ 75.6%

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

   5. Simplified 75.6%

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

   if -3.6e70 < A < 4.6000000000000004e-78 or 9.0000000000000001e-56 < A < 0.859999999999999987

   1. Initial program 58.6%

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

      1. +-commutative 58.6%

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

      2. unpow2 58.6%

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

      3. unpow2 58.6%

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

      4. hypot-udef 79.9%

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

      5. associate--r+ 79.8%

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

      6. associate-/r/ 79.8%

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

      7. associate--r+ 79.9%

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

      8. hypot-udef 58.6%

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

      9. unpow2 58.6%

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

      10. unpow2 58.6%

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

      11. +-commutative 58.6%

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

      12. unpow2 58.6%

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

      13. unpow2 58.6%

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

      14. hypot-def 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in A around 0 57.7%

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

      1. unpow2 57.7%

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

      2. unpow2 57.7%

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

      3. hypot-def 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in B around inf 58.4%

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

   if 4.6000000000000004e-78 < A < 9.0000000000000001e-56

   1. Initial program 6.8%

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

      1. +-commutative 6.8%

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

      2. unpow2 6.8%

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

      3. unpow2 6.8%

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

      4. hypot-udef 24.6%

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

      5. associate--r+ 24.6%

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

      6. associate-/r/ 24.6%

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

      7. associate--r+ 24.6%

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

      8. hypot-udef 6.8%

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

      9. unpow2 6.8%

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

      10. unpow2 6.8%

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

      11. +-commutative 6.8%

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

      12. unpow2 6.8%

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

      13. unpow2 6.8%

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

      14. hypot-def 24.6%

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

   4. Applied egg-rr 24.6%

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

   5. Taylor expanded in A around 0 6.8%

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

      1. unpow2 6.8%

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

      2. unpow2 6.8%

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

      3. hypot-def 24.6%

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

   7. Simplified 24.6%

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

   8. Taylor expanded in B around 0 83.1%

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

      1. *-commutative 83.1%

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

   10. Simplified 83.1%

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

   if 0.859999999999999987 < A

   1. Initial program 77.9%

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

   3. Taylor expanded in A around inf 72.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.6 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.86:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 6.2 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 34:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))
   (if (<= A -5.6e+68)
     (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
     (if (<= A 6.2e-80)
       t_0
       (if (<= A 8.5e-56)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= A 34.0) t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double tmp;
	if (A <= -5.6e+68) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= 6.2e-80) {
		tmp = t_0;
	} else if (A <= 8.5e-56) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (A <= 34.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double tmp;
	if (A <= -5.6e+68) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= 6.2e-80) {
		tmp = t_0;
	} else if (A <= 8.5e-56) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (A <= 34.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	tmp = 0
	if A <= -5.6e+68:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= 6.2e-80:
		tmp = t_0
	elif A <= 8.5e-56:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif A <= 34.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	tmp = 0.0
	if (A <= -5.6e+68)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= 6.2e-80)
		tmp = t_0;
	elseif (A <= 8.5e-56)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (A <= 34.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	tmp = 0.0;
	if (A <= -5.6e+68)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= 6.2e-80)
		tmp = t_0;
	elseif (A <= 8.5e-56)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (A <= 34.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.6e+68], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.2e-80], t$95$0, If[LessEqual[A, 8.5e-56], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 34.0], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.6e68

   1. Initial program 21.7%

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

   4. Applied egg-rr 58.0%

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

   5. Taylor expanded in A around -inf 74.7%

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

      1. associate-*r/ 74.7%

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

   7. Simplified 74.7%

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

      1. associate-/r/ 74.8%

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

      2. associate-/l* 74.8%

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

   9. Applied egg-rr 74.8%

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

   if -5.6e68 < A < 6.20000000000000032e-80 or 8.49999999999999932e-56 < A < 34

   1. Initial program 58.7%

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

      1. +-commutative 58.7%

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

      2. unpow2 58.7%

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

      3. unpow2 58.7%

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

      4. hypot-udef 80.4%

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

      5. associate--r+ 80.3%

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

      6. associate-/r/ 80.3%

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

      7. associate--r+ 80.4%

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

      8. hypot-udef 58.7%

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

      9. unpow2 58.7%

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

      10. unpow2 58.7%

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

      11. +-commutative 58.7%

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

      12. unpow2 58.7%

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

      13. unpow2 58.7%

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

      14. hypot-def 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in A around 0 57.8%

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

      1. unpow2 57.8%

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

      2. unpow2 57.8%

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

      3. hypot-def 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in B around inf 58.5%

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

   if 6.20000000000000032e-80 < A < 8.49999999999999932e-56

   1. Initial program 6.8%

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

      1. +-commutative 6.8%

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

      2. unpow2 6.8%

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

      3. unpow2 6.8%

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

      4. hypot-udef 24.6%

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

      5. associate--r+ 24.6%

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

      6. associate-/r/ 24.6%

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

      7. associate--r+ 24.6%

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

      8. hypot-udef 6.8%

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

      9. unpow2 6.8%

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

      10. unpow2 6.8%

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

      11. +-commutative 6.8%

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

      12. unpow2 6.8%

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

      13. unpow2 6.8%

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

      14. hypot-def 24.6%

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

   4. Applied egg-rr 24.6%

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

   5. Taylor expanded in A around 0 6.8%

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

      1. unpow2 6.8%

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

      2. unpow2 6.8%

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

      3. hypot-def 24.6%

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

   7. Simplified 24.6%

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

   8. Taylor expanded in B around 0 83.1%

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

      1. *-commutative 83.1%

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

   10. Simplified 83.1%

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

   if 34 < A

   1. Initial program 77.9%

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

   3. Taylor expanded in A around inf 72.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 6.2 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 34:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.38 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;A \leq 34:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))
   (if (<= A -1.7e+68)
     (* (/ 180.0 PI) (atan (/ 0.5 (/ A B))))
     (if (<= A 1.25e-80)
       t_0
       (if (<= A 1.38e-55)
         (/ 180.0 (/ PI (atan (* -0.5 (/ B C)))))
         (if (<= A 34.0) t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double tmp;
	if (A <= -1.7e+68) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 / (A / B)));
	} else if (A <= 1.25e-80) {
		tmp = t_0;
	} else if (A <= 1.38e-55) {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	} else if (A <= 34.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double tmp;
	if (A <= -1.7e+68) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 / (A / B)));
	} else if (A <= 1.25e-80) {
		tmp = t_0;
	} else if (A <= 1.38e-55) {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	} else if (A <= 34.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	tmp = 0
	if A <= -1.7e+68:
		tmp = (180.0 / math.pi) * math.atan((0.5 / (A / B)))
	elif A <= 1.25e-80:
		tmp = t_0
	elif A <= 1.38e-55:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	elif A <= 34.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	tmp = 0.0
	if (A <= -1.7e+68)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 / Float64(A / B))));
	elseif (A <= 1.25e-80)
		tmp = t_0;
	elseif (A <= 1.38e-55)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	elseif (A <= 34.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	tmp = 0.0;
	if (A <= -1.7e+68)
		tmp = (180.0 / pi) * atan((0.5 / (A / B)));
	elseif (A <= 1.25e-80)
		tmp = t_0;
	elseif (A <= 1.38e-55)
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	elseif (A <= 34.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.7e+68], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-80], t$95$0, If[LessEqual[A, 1.38e-55], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 34.0], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.70000000000000008e68

   1. Initial program 21.7%

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

   4. Applied egg-rr 58.0%

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

   5. Taylor expanded in A around -inf 74.7%

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

      1. associate-*r/ 74.7%

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

   7. Simplified 74.7%

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

      1. associate-/r/ 74.8%

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

      2. associate-/l* 74.8%

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

   9. Applied egg-rr 74.8%

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

   if -1.70000000000000008e68 < A < 1.25e-80 or 1.3799999999999999e-55 < A < 34

   1. Initial program 58.7%

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

      1. +-commutative 58.7%

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

      2. unpow2 58.7%

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

      3. unpow2 58.7%

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

      4. hypot-udef 80.4%

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

      5. associate--r+ 80.3%

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

      6. associate-/r/ 80.3%

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

      7. associate--r+ 80.4%

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

      8. hypot-udef 58.7%

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

      9. unpow2 58.7%

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

      10. unpow2 58.7%

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

      11. +-commutative 58.7%

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

      12. unpow2 58.7%

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

      13. unpow2 58.7%

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

      14. hypot-def 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in A around 0 57.8%

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

      1. unpow2 57.8%

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

      2. unpow2 57.8%

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

      3. hypot-def 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in B around inf 58.5%

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

   if 1.25e-80 < A < 1.3799999999999999e-55

   1. Initial program 6.8%

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

   4. Applied egg-rr 24.6%

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

   5. Taylor expanded in A around 0 6.8%

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

      1. unpow2 6.8%

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

      2. unpow2 6.8%

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

      3. hypot-def 24.6%

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

   7. Simplified 24.6%

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

   8. Taylor expanded in C around inf 83.4%

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

   if 34 < A

   1. Initial program 77.9%

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

   3. Taylor expanded in A around inf 72.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.38 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{elif}\;A \leq 34:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -6.2e-51)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -9e-198)
       t_0
       (if (<= B 4.2e-233)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 2.4e-65) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -6.2e-51) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9e-198) {
		tmp = t_0;
	} else if (B <= 4.2e-233) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.4e-65) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -6.2e-51) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9e-198) {
		tmp = t_0;
	} else if (B <= 4.2e-233) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.4e-65) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -6.2e-51:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9e-198:
		tmp = t_0
	elif B <= 4.2e-233:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.4e-65:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -6.2e-51)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9e-198)
		tmp = t_0;
	elseif (B <= 4.2e-233)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.4e-65)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -6.2e-51)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9e-198)
		tmp = t_0;
	elseif (B <= 4.2e-233)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.4e-65)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.2e-51], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9e-198], t$95$0, If[LessEqual[B, 4.2e-233], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-65], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.1999999999999995e-51

   1. Initial program 46.1%

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

   3. Taylor expanded in B around -inf 51.8%

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

   if -6.1999999999999995e-51 < B < -8.9999999999999996e-198 or 4.1999999999999997e-233 < B < 2.4000000000000002e-65

   1. Initial program 65.8%

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

      1. associate--l- 65.5%

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

      2. add-cube-cbrt 65.4%

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

      3. +-commutative 65.4%

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

      4. unpow2 65.4%

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

      5. unpow2 65.4%

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

      6. hypot-udef 68.2%

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

      7. fma-neg 65.5%

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

      8. *-un-lft-identity 65.5%

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

      9. *-commutative 65.5%

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

      10. pow2 65.5%

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

      11. *-commutative 65.5%

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

      12. *-un-lft-identity 65.5%

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

      13. hypot-udef 65.4%

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

      14. unpow2 65.4%

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

      15. unpow2 65.4%

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

      16. +-commutative 65.4%

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

      17. unpow2 65.4%

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

      18. unpow2 65.4%

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

   4. Applied egg-rr 65.5%

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

   5. Taylor expanded in C around -inf 49.7%

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

   if -8.9999999999999996e-198 < B < 4.1999999999999997e-233

   1. Initial program 51.4%

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

   3. Taylor expanded in C around inf 51.5%

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

      1. associate-*r/ 51.5%

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

      2. distribute-rgt1-in 51.5%

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

      3. metadata-eval 51.5%

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

      4. mul0-lft 51.5%

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

      5. metadata-eval 51.5%

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

   5. Simplified 51.5%

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

   if 2.4000000000000002e-65 < B

   1. Initial program 54.4%

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

   3. Taylor expanded in B around inf 57.9%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B + C}{B}\right)}}\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-244} \lor \neg \left(B \leq 2.3 \cdot 10^{-233}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-29)
   (/ 180.0 (/ PI (atan (/ (+ B C) B))))
   (if (or (<= B -1.42e-244) (not (<= B 2.3e-233)))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))
     (* 180.0 (/ (atan (/ 0.0 B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-29) {
		tmp = 180.0 / (((double) M_PI) / atan(((B + C) / B)));
	} else if ((B <= -1.42e-244) || !(B <= 2.3e-233)) {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-29) {
		tmp = 180.0 / (Math.PI / Math.atan(((B + C) / B)));
	} else if ((B <= -1.42e-244) || !(B <= 2.3e-233)) {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-29:
		tmp = 180.0 / (math.pi / math.atan(((B + C) / B)))
	elif (B <= -1.42e-244) or not (B <= 2.3e-233):
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-29)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B + C) / B))));
	elseif ((B <= -1.42e-244) || !(B <= 2.3e-233))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-29)
		tmp = 180.0 / (pi / atan(((B + C) / B)));
	elseif ((B <= -1.42e-244) || ~((B <= 2.3e-233)))
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-29], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, -1.42e-244], N[Not[LessEqual[B, 2.3e-233]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -9.99999999999999943e-30

   1. Initial program 44.5%

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

   4. Applied egg-rr 71.6%

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

   5. Taylor expanded in A around 0 37.5%

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

      1. unpow2 37.5%

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

      2. unpow2 37.5%

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

      3. hypot-def 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in B around -inf 64.1%

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

      1. +-commutative 64.1%

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

   10. Simplified 64.1%

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

   if -9.99999999999999943e-30 < B < -1.42000000000000003e-244 or 2.3000000000000002e-233 < B

   1. Initial program 59.6%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in B around inf 70.1%

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

      1. +-commutative 70.1%

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

   7. Simplified 70.1%

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

   if -1.42000000000000003e-244 < B < 2.3000000000000002e-233

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. distribute-rgt1-in 55.7%

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

      3. metadata-eval 55.7%

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

      4. mul0-lft 55.7%

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

      5. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B + C}{B}\right)}}\\ \mathbf{elif}\;B \leq -1.42 \cdot 10^{-244} \lor \neg \left(B \leq 2.3 \cdot 10^{-233}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.5 \cdot 10^{-117}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.15 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.5e-117)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C -2.15e-253)
     (* 180.0 (/ (atan -1.0) PI))
     (if (<= C 1.05e-198)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.5e-117) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= -2.15e-253) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 1.05e-198) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.5e-117) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= -2.15e-253) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 1.05e-198) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.5e-117:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= -2.15e-253:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 1.05e-198:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.5e-117)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= -2.15e-253)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 1.05e-198)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.5e-117)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= -2.15e-253)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 1.05e-198)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.5e-117], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.15e-253], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.05e-198], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -3.4999999999999998e-117

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. unpow2 73.2%

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

      3. unpow2 73.2%

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

      4. hypot-udef 90.1%

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

      5. associate--r+ 88.3%

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

      6. associate-/r/ 88.3%

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

      7. associate--r+ 90.1%

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

      8. hypot-udef 73.2%

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

      9. unpow2 73.2%

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

      10. unpow2 73.2%

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

      11. +-commutative 73.2%

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

      12. unpow2 73.2%

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

      13. unpow2 73.2%

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

      14. hypot-def 90.1%

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

   4. Applied egg-rr 90.1%

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

   5. Taylor expanded in A around 0 68.9%

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

      1. unpow2 68.9%

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

      2. unpow2 68.9%

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

      3. hypot-def 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in B around -inf 67.9%

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

   if -3.4999999999999998e-117 < C < -2.1500000000000001e-253

   1. Initial program 80.0%

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

   3. Taylor expanded in B around inf 46.5%

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

   if -2.1500000000000001e-253 < C < 1.04999999999999996e-198

   1. Initial program 59.5%

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

   3. Taylor expanded in B around -inf 47.8%

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

   if 1.04999999999999996e-198 < C

   1. Initial program 32.4%

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

      1. +-commutative 32.4%

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

      2. unpow2 32.4%

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

      3. unpow2 32.4%

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

      4. hypot-udef 63.7%

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

      5. associate--r+ 56.3%

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

      6. associate-/r/ 56.3%

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

      7. associate--r+ 63.7%

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

      8. hypot-udef 32.4%

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

      9. unpow2 32.4%

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

      10. unpow2 32.4%

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

      11. +-commutative 32.4%

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

      12. unpow2 32.4%

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

      13. unpow2 32.4%

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

      14. hypot-def 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in A around 0 23.0%

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

      1. unpow2 23.0%

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

      2. unpow2 23.0%

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

      3. hypot-def 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in B around 0 56.9%

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

      1. *-commutative 56.9%

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

   10. Simplified 56.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.5 \cdot 10^{-117}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.15 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.05 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-244}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-244)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 1.4e-237)
     (* 180.0 (/ (atan (/ 1.0 (+ 1.0 (/ (- A C) B)))) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-244) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 1.4e-237) {
		tmp = 180.0 * (atan((1.0 / (1.0 + ((A - C) / B)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-244) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 1.4e-237) {
		tmp = 180.0 * (Math.atan((1.0 / (1.0 + ((A - C) / B)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.8e-244:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 1.4e-237:
		tmp = 180.0 * (math.atan((1.0 / (1.0 + ((A - C) / B)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.8e-244)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 1.4e-237)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 / Float64(1.0 + Float64(Float64(A - C) / B)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.8e-244)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 1.4e-237)
		tmp = 180.0 * (atan((1.0 / (1.0 + ((A - C) / B)))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.8e-244], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-237], N[(180.0 * N[(N[ArcTan[N[(1.0 / N[(1.0 + N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.8000000000000001e-244

   1. Initial program 53.9%

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

   4. Applied egg-rr 72.0%

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

   5. Taylor expanded in B around -inf 64.8%

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

   if -3.8000000000000001e-244 < B < 1.39999999999999999e-237

   1. Initial program 49.2%

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

      1. +-commutative 49.2%

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

      2. unpow2 49.2%

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

      3. unpow2 49.2%

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

      4. hypot-udef 84.7%

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

      5. associate--r+ 55.5%

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

      6. associate-/r/ 55.5%

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

      7. associate--r+ 84.7%

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

      8. hypot-udef 49.2%

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

      9. unpow2 49.2%

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

      10. unpow2 49.2%

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

      11. +-commutative 49.2%

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

      12. unpow2 49.2%

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

      13. unpow2 49.2%

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

      14. hypot-def 84.7%

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

   4. Applied egg-rr 84.7%

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

   5. Taylor expanded in B around -inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   7. Simplified 57.4%

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

   if 1.39999999999999999e-237 < B

   1. Initial program 57.6%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in B around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-244}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2 + A \cdot 2}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.5e-198)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 2.7e-240)
     (* 180.0 (/ (atan (/ B (+ (* C -2.0) (* A 2.0)))) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-198) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 2.7e-240) {
		tmp = 180.0 * (atan((B / ((C * -2.0) + (A * 2.0)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-198) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 2.7e-240) {
		tmp = 180.0 * (Math.atan((B / ((C * -2.0) + (A * 2.0)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.5e-198:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 2.7e-240:
		tmp = 180.0 * (math.atan((B / ((C * -2.0) + (A * 2.0)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.5e-198)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 2.7e-240)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(Float64(C * -2.0) + Float64(A * 2.0)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.5e-198)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 2.7e-240)
		tmp = 180.0 * (atan((B / ((C * -2.0) + (A * 2.0)))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.5e-198], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-240], N[(180.0 * N[(N[ArcTan[N[(B / N[(N[(C * -2.0), $MachinePrecision] + N[(A * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.4999999999999994e-198

   1. Initial program 53.5%

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

   4. Applied egg-rr 72.0%

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

   5. Taylor expanded in B around -inf 66.7%

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

   if -8.4999999999999994e-198 < B < 2.70000000000000018e-240

   1. Initial program 51.4%

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

      1. +-commutative 51.4%

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

      2. unpow2 51.4%

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

      3. unpow2 51.4%

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

      4. hypot-udef 82.1%

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

      5. associate--r+ 56.3%

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

      6. associate-/r/ 56.3%

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

      7. associate--r+ 82.1%

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

      8. hypot-udef 51.4%

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

      9. unpow2 51.4%

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

      10. unpow2 51.4%

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

      11. +-commutative 51.4%

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

      12. unpow2 51.4%

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

      13. unpow2 51.4%

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

      14. hypot-def 82.1%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in A around -inf 58.3%

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

   6. Taylor expanded in B around 0 68.9%

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

   if 2.70000000000000018e-240 < B

   1. Initial program 57.6%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in B around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2 + A \cdot 2}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.15e-244)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B 1.2e-238)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-244) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= 1.2e-238) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-244) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= 1.2e-238) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.15e-244:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= 1.2e-238:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.15e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= 1.2e-238)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.15e-244)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= 1.2e-238)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.15e-244], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.2e-238], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.15e-244

   1. Initial program 53.9%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in B around -inf 64.8%

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

      1. neg-mul-1 64.8%

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

      2. unsub-neg 64.8%

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

   7. Simplified 64.8%

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

   if -1.15e-244 < B < 1.1999999999999999e-238

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. distribute-rgt1-in 55.7%

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

      3. metadata-eval 55.7%

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

      4. mul0-lft 55.7%

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

      5. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

   if 1.1999999999999999e-238 < B

   1. Initial program 57.6%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in B around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-243}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.4e-243)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 6.4e-242)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-243) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 6.4e-242) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-243) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 6.4e-242) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.4e-243:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 6.4e-242:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.4e-243)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 6.4e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.4e-243)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 6.4e-242)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.4e-243], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.4e-242], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.40000000000000021e-243

   1. Initial program 53.9%

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

   4. Applied egg-rr 72.0%

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

   5. Taylor expanded in B around -inf 64.8%

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

   if -5.40000000000000021e-243 < B < 6.39999999999999997e-242

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. distribute-rgt1-in 55.7%

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

      3. metadata-eval 55.7%

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

      4. mul0-lft 55.7%

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

      5. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

   if 6.39999999999999997e-242 < B

   1. Initial program 57.6%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in B around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-243}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.75e-147)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.6e-52)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.75e-147) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.6e-52) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.75e-147) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.6e-52) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.75e-147:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.6e-52:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.75e-147)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.6e-52)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.75e-147)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.6e-52)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.75e-147], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-52], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.75000000000000002e-147

   1. Initial program 52.6%

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

   3. Taylor expanded in B around -inf 40.1%

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

   if -1.75000000000000002e-147 < B < 1.60000000000000005e-52

   1. Initial program 57.7%

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

   3. Taylor expanded in C around inf 37.9%

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

      1. associate-*r/ 37.9%

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

      2. distribute-rgt1-in 37.9%

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

      3. metadata-eval 37.9%

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

      4. mul0-lft 37.9%

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

      5. metadata-eval 37.9%

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

   5. Simplified 37.9%

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

   if 1.60000000000000005e-52 < B

   1. Initial program 55.0%

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

   3. Taylor expanded in B around inf 60.3%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 53.8%

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

   3. Taylor expanded in B around -inf 32.2%

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

   if -1.999999999999994e-310 < B

   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 43.6%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.8% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.0%

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

3. Taylor expanded in B around inf 22.6%

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

4. Final simplification 22.6%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(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)))