ABCF->ab-angle angle

Percentage Accurate: 56.0% → 83.5%

Time: 21.2s

Alternatives: 14

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{+165}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.4e+165)
   (/ 1.0 (/ (/ PI 180.0) (atan (* 0.5 (/ B A)))))
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e+165) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((0.5 * (B / A))));
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e+165) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((0.5 * (B / A))));
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.4e+165:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((0.5 * (B / A))))
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.4e+165)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.4e+165)
		tmp = 1.0 / ((pi / 180.0) / atan((0.5 * (B / A))));
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.4e+165], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.40000000000000011e165

   1. Initial program 12.4%

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

   4. Applied egg-rr 60.3%

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

      1. associate-/r* 60.3%

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

      2. associate--l- 22.5%

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

   6. Simplified 22.5%

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

   7. Taylor expanded in A around -inf 80.9%

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

   if -3.40000000000000011e165 < A

   1. Initial program 65.4%

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

      1. associate-*r/ 65.3%

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

      2. associate-*l/ 65.3%

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

      3. *-un-lft-identity 65.3%

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

      4. unpow2 65.3%

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

      5. unpow2 65.3%

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

      6. hypot-def 89.0%

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

   4. Applied egg-rr 89.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{+165}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-184}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e+161)
   (/ 1.0 (/ (/ PI 180.0) (atan (* 0.5 (/ B A)))))
   (if (<= A 2e-184)
     (/ 1.0 (/ PI (/ (atan (/ (- C (hypot B C)) B)) 0.005555555555555556)))
     (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e+161) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((0.5 * (B / A))));
	} else if (A <= 2e-184) {
		tmp = 1.0 / (((double) M_PI) / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	} 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 <= -9.5e+161) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((0.5 * (B / A))));
	} else if (A <= 2e-184) {
		tmp = 1.0 / (Math.PI / (Math.atan(((C - Math.hypot(B, C)) / B)) / 0.005555555555555556));
	} 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 <= -9.5e+161:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((0.5 * (B / A))))
	elif A <= 2e-184:
		tmp = 1.0 / (math.pi / (math.atan(((C - math.hypot(B, C)) / B)) / 0.005555555555555556))
	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 <= -9.5e+161)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 2e-184)
		tmp = Float64(1.0 / Float64(pi / Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / 0.005555555555555556)));
	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 <= -9.5e+161)
		tmp = 1.0 / ((pi / 180.0) / atan((0.5 * (B / A))));
	elseif (A <= 2e-184)
		tmp = 1.0 / (pi / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	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, -9.5e+161], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-184], N[(1.0 / N[(Pi / N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $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 3 regimes

2. if A < -9.50000000000000061e161

   1. Initial program 12.4%

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

   4. Applied egg-rr 60.3%

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

      1. associate-/r* 60.3%

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

      2. associate--l- 22.5%

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

   6. Simplified 22.5%

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

   7. Taylor expanded in A around -inf 80.9%

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

   if -9.50000000000000061e161 < A < 2.0000000000000001e-184

   1. Initial program 57.9%

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

   4. Applied egg-rr 83.4%

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

      1. associate-/r* 83.4%

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

      2. associate--l- 76.4%

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

   6. Simplified 76.4%

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

      1. inv-pow 76.4%

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

      2. add-sqr-sqrt 42.4%

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

      3. sqrt-pow1 42.7%

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

      4. div-inv 42.7%

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

      5. metadata-eval 42.7%

         \[\leadsto {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      6. metadata-eval 42.7%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      7. sqrt-pow1 42.4%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot \color{blue}{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)}} \]

      8. div-inv 42.4%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\color{blue}{\pi \cdot \frac{1}{180}}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 42.4%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. metadata-eval 42.4%

          \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \]

   8. Applied egg-rr 42.4%

      \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5}} \]
   9. Step-by-step derivation

      1. pow-sqr 76.4%

         \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 76.4%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-1}} \]

      3. unpow-1 76.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}}} \]

      4. associate-/l* 76.4%

         \[\leadsto \frac{1}{\color{blue}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   10. Simplified 76.4%

       \[\leadsto \color{blue}{\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   11. Taylor expanded in A around 0 54.1%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{0.005555555555555556}}} \]
   12. Step-by-step derivation

       1. unpow2 54.1%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{0.005555555555555556}}} \]

       2. unpow2 54.1%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{0.005555555555555556}}} \]

       3. hypot-def 79.7%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   13. Simplified 79.7%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   if 2.0000000000000001e-184 < A

   1. Initial program 74.0%

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

   3. Simplified 95.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-184}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+108}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.4e-17)
   (/ 1.0 (/ PI (/ (atan (/ (- C (hypot B C)) B)) 0.005555555555555556)))
   (if (<= C 1.85e+108)
     (/ 1.0 (/ (/ PI 180.0) (atan (/ (- (- A) (hypot B A)) B))))
     (* (atan (* B (/ -0.5 C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 1.0 / (((double) M_PI) / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 1.85e+108) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan(((-A - hypot(B, A)) / B)));
	} else {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 1.0 / (Math.PI / (Math.atan(((C - Math.hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 1.85e+108) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan(((-A - Math.hypot(B, A)) / B)));
	} else {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.4e-17:
		tmp = 1.0 / (math.pi / (math.atan(((C - math.hypot(B, C)) / B)) / 0.005555555555555556))
	elif C <= 1.85e+108:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan(((-A - math.hypot(B, A)) / B)))
	else:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.4e-17)
		tmp = Float64(1.0 / Float64(pi / Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / 0.005555555555555556)));
	elseif (C <= 1.85e+108)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B))));
	else
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.4e-17)
		tmp = 1.0 / (pi / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	elseif (C <= 1.85e+108)
		tmp = 1.0 / ((pi / 180.0) / atan(((-A - hypot(B, A)) / B)));
	else
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.4e-17], N[(1.0 / N[(Pi / N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e+108], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.3999999999999999e-17

   1. Initial program 84.4%

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

   4. Applied egg-rr 95.0%

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

      1. associate-/r* 95.0%

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

      2. associate--l- 92.6%

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

   6. Simplified 92.6%

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

      1. inv-pow 92.6%

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

      2. add-sqr-sqrt 50.8%

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

      3. sqrt-pow1 50.9%

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

      4. div-inv 50.9%

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

      5. metadata-eval 50.9%

         \[\leadsto {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      6. metadata-eval 50.9%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      7. sqrt-pow1 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot \color{blue}{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)}} \]

      8. div-inv 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\color{blue}{\pi \cdot \frac{1}{180}}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. metadata-eval 50.8%

          \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \]

   8. Applied egg-rr 50.8%

      \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5}} \]
   9. Step-by-step derivation

      1. pow-sqr 92.6%

         \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 92.6%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-1}} \]

      3. unpow-1 92.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}}} \]

      4. associate-/l* 92.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   10. Simplified 92.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   11. Taylor expanded in A around 0 84.4%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{0.005555555555555556}}} \]
   12. Step-by-step derivation

       1. unpow2 84.4%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{0.005555555555555556}}} \]

       2. unpow2 84.4%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{0.005555555555555556}}} \]

       3. hypot-def 90.8%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   13. Simplified 90.8%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   if -1.3999999999999999e-17 < C < 1.8499999999999999e108

   1. Initial program 57.3%

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

   4. Applied egg-rr 85.9%

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

      1. associate-/r* 86.0%

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

      2. associate--l- 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in C around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. unpow2 56.0%

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

      4. unpow2 56.0%

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

      5. hypot-def 84.6%

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

   9. Simplified 84.6%

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

   if 1.8499999999999999e108 < C

   1. Initial program 23.1%

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

   3. Taylor expanded in A around 0 23.1%

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

      1. unpow2 23.1%

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

      2. unpow2 23.1%

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

      3. hypot-def 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in C around inf 71.4%

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

   7. Taylor expanded in B around 0 76.8%

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

      1. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

   10. Taylor expanded in B around 0 76.8%

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

       1. associate-*r/ 76.8%

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

       2. associate-*l/ 76.9%

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

       3. metadata-eval 76.9%

          \[\leadsto \frac{\color{blue}{\frac{1}{0.005555555555555556}}}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       4. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \pi}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       5. *-commutative 76.9%

          \[\leadsto \frac{1}{\color{blue}{\pi \cdot 0.005555555555555556}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       6. *-commutative 76.9%

          \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{1}{\pi \cdot 0.005555555555555556}} \]

       7. associate-*r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       8. associate-/l* 77.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       9. associate-/r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       10. *-commutative 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \frac{1}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       11. associate-/r* 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \color{blue}{\frac{\frac{1}{0.005555555555555556}}{\pi}} \]

       12. metadata-eval 76.9%

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

   12. Simplified 76.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+108}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.56 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.15 \cdot 10^{+105}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.56e-17)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= C 3.15e+105)
     (* -180.0 (/ (atan (/ (+ A (hypot B A)) B)) PI))
     (* (atan (* B (/ -0.5 C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.56e-17) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (C <= 3.15e+105) {
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.56e-17) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (C <= 3.15e+105) {
		tmp = -180.0 * (Math.atan(((A + Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.56e-17:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif C <= 3.15e+105:
		tmp = -180.0 * (math.atan(((A + math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.56e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (C <= 3.15e+105)
		tmp = Float64(-180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.56e-17)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (C <= 3.15e+105)
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / pi);
	else
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.56e-17], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.15e+105], N[(-180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.56000000000000002e-17

   1. Initial program 84.4%

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

   3. Taylor expanded in B around -inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. div-sub 81.6%

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

   5. Simplified 81.6%

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

   if -1.56000000000000002e-17 < C < 3.14999999999999977e105

   1. Initial program 57.3%

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

   4. Applied egg-rr 85.9%

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

      1. associate-/r* 86.0%

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

      2. associate--l- 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in C around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. unpow2 56.0%

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

      4. unpow2 56.0%

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

      5. hypot-def 84.6%

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

   9. Simplified 84.6%

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

       1. expm1-log1p-u 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)\right)} \]

       2. expm1-udef 47.2%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)} - 1} \]

       3. associate-/r/ 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{1}{\frac{\pi}{180}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}\right)} - 1 \]

       4. div-inv 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{\pi \cdot \frac{1}{180}}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       5. metadata-eval 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot \color{blue}{0.005555555555555556}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       6. distribute-frac-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}\right)} - 1 \]

       7. atan-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}\right)} - 1 \]

   11. Applied egg-rr 47.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)\right)} \]

       2. expm1-log1p 84.6%

          \[\leadsto \color{blue}{\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)} \]

       3. associate-*l/ 84.6%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}{\pi \cdot 0.005555555555555556}} \]

       4. *-lft-identity 84.6%

          \[\leadsto \frac{\color{blue}{-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       5. neg-mul-1 84.6%

          \[\leadsto \frac{\color{blue}{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       6. *-commutative 84.6%

          \[\leadsto \frac{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       7. times-frac 84.6%

          \[\leadsto \color{blue}{\frac{-1}{0.005555555555555556} \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}} \]

       8. metadata-eval 84.6%

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

   13. Simplified 84.6%

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

   if 3.14999999999999977e105 < C

   1. Initial program 23.1%

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

   3. Taylor expanded in A around 0 23.1%

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

      1. unpow2 23.1%

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

      2. unpow2 23.1%

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

      3. hypot-def 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in C around inf 71.4%

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

   7. Taylor expanded in B around 0 76.8%

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

      1. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

   10. Taylor expanded in B around 0 76.8%

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

       1. associate-*r/ 76.8%

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

       2. associate-*l/ 76.9%

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

       3. metadata-eval 76.9%

          \[\leadsto \frac{\color{blue}{\frac{1}{0.005555555555555556}}}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       4. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \pi}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       5. *-commutative 76.9%

          \[\leadsto \frac{1}{\color{blue}{\pi \cdot 0.005555555555555556}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       6. *-commutative 76.9%

          \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{1}{\pi \cdot 0.005555555555555556}} \]

       7. associate-*r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       8. associate-/l* 77.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       9. associate-/r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       10. *-commutative 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \frac{1}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       11. associate-/r* 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \color{blue}{\frac{\frac{1}{0.005555555555555556}}{\pi}} \]

       12. metadata-eval 76.9%

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

   12. Simplified 76.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.56 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.15 \cdot 10^{+105}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{+108}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.4e-17)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 4.4e+108)
     (* -180.0 (/ (atan (/ (+ A (hypot B A)) B)) PI))
     (* (atan (* B (/ -0.5 C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 4.4e+108) {
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 4.4e+108) {
		tmp = -180.0 * (Math.atan(((A + Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.4e-17:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 4.4e+108:
		tmp = -180.0 * (math.atan(((A + math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.4e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 4.4e+108)
		tmp = Float64(-180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.4e-17)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 4.4e+108)
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / pi);
	else
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.4e-17], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.4e+108], N[(-180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.3999999999999999e-17

   1. Initial program 84.4%

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

   3. Taylor expanded in A around 0 84.4%

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

      1. unpow2 84.4%

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

      2. unpow2 84.4%

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

      3. hypot-def 90.8%

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

   5. Simplified 90.8%

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

   if -1.3999999999999999e-17 < C < 4.4000000000000003e108

   1. Initial program 57.3%

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

   4. Applied egg-rr 85.9%

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

      1. associate-/r* 86.0%

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

      2. associate--l- 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in C around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. unpow2 56.0%

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

      4. unpow2 56.0%

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

      5. hypot-def 84.6%

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

   9. Simplified 84.6%

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

       1. expm1-log1p-u 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)\right)} \]

       2. expm1-udef 47.2%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)} - 1} \]

       3. associate-/r/ 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{1}{\frac{\pi}{180}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}\right)} - 1 \]

       4. div-inv 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{\pi \cdot \frac{1}{180}}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       5. metadata-eval 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot \color{blue}{0.005555555555555556}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       6. distribute-frac-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}\right)} - 1 \]

       7. atan-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}\right)} - 1 \]

   11. Applied egg-rr 47.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)\right)} \]

       2. expm1-log1p 84.6%

          \[\leadsto \color{blue}{\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)} \]

       3. associate-*l/ 84.6%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}{\pi \cdot 0.005555555555555556}} \]

       4. *-lft-identity 84.6%

          \[\leadsto \frac{\color{blue}{-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       5. neg-mul-1 84.6%

          \[\leadsto \frac{\color{blue}{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       6. *-commutative 84.6%

          \[\leadsto \frac{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       7. times-frac 84.6%

          \[\leadsto \color{blue}{\frac{-1}{0.005555555555555556} \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}} \]

       8. metadata-eval 84.6%

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

   13. Simplified 84.6%

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

   if 4.4000000000000003e108 < C

   1. Initial program 23.1%

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

   3. Taylor expanded in A around 0 23.1%

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

      1. unpow2 23.1%

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

      2. unpow2 23.1%

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

      3. hypot-def 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in C around inf 71.4%

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

   7. Taylor expanded in B around 0 76.8%

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

      1. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

   10. Taylor expanded in B around 0 76.8%

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

       1. associate-*r/ 76.8%

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

       2. associate-*l/ 76.9%

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

       3. metadata-eval 76.9%

          \[\leadsto \frac{\color{blue}{\frac{1}{0.005555555555555556}}}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       4. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \pi}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       5. *-commutative 76.9%

          \[\leadsto \frac{1}{\color{blue}{\pi \cdot 0.005555555555555556}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       6. *-commutative 76.9%

          \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{1}{\pi \cdot 0.005555555555555556}} \]

       7. associate-*r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       8. associate-/l* 77.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       9. associate-/r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       10. *-commutative 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \frac{1}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       11. associate-/r* 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \color{blue}{\frac{\frac{1}{0.005555555555555556}}{\pi}} \]

       12. metadata-eval 76.9%

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

   12. Simplified 76.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{+108}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.4e-17)
   (/ 1.0 (/ PI (/ (atan (/ (- C (hypot B C)) B)) 0.005555555555555556)))
   (if (<= C 2.05e+99)
     (* -180.0 (/ (atan (/ (+ A (hypot B A)) B)) PI))
     (* (atan (* B (/ -0.5 C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 1.0 / (((double) M_PI) / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 2.05e+99) {
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.4e-17) {
		tmp = 1.0 / (Math.PI / (Math.atan(((C - Math.hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 2.05e+99) {
		tmp = -180.0 * (Math.atan(((A + Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.4e-17:
		tmp = 1.0 / (math.pi / (math.atan(((C - math.hypot(B, C)) / B)) / 0.005555555555555556))
	elif C <= 2.05e+99:
		tmp = -180.0 * (math.atan(((A + math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.4e-17)
		tmp = Float64(1.0 / Float64(pi / Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / 0.005555555555555556)));
	elseif (C <= 2.05e+99)
		tmp = Float64(-180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.4e-17)
		tmp = 1.0 / (pi / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	elseif (C <= 2.05e+99)
		tmp = -180.0 * (atan(((A + hypot(B, A)) / B)) / pi);
	else
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.4e-17], N[(1.0 / N[(Pi / N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e+99], N[(-180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.3999999999999999e-17

   1. Initial program 84.4%

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

   4. Applied egg-rr 95.0%

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

      1. associate-/r* 95.0%

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

      2. associate--l- 92.6%

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

   6. Simplified 92.6%

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

      1. inv-pow 92.6%

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

      2. add-sqr-sqrt 50.8%

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

      3. sqrt-pow1 50.9%

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

      4. div-inv 50.9%

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

      5. metadata-eval 50.9%

         \[\leadsto {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      6. metadata-eval 50.9%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \cdot \sqrt{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-1}} \]

      7. sqrt-pow1 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot \color{blue}{{\left(\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)}} \]

      8. div-inv 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\color{blue}{\pi \cdot \frac{1}{180}}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 50.8%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot \color{blue}{0.005555555555555556}}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. metadata-eval 50.8%

          \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-0.5}} \]

   8. Applied egg-rr 50.8%

      \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5} \cdot {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{-0.5}} \]
   9. Step-by-step derivation

      1. pow-sqr 92.6%

         \[\leadsto \color{blue}{{\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 92.6%

         \[\leadsto {\left(\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}\right)}^{\color{blue}{-1}} \]

      3. unpow-1 92.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\pi \cdot 0.005555555555555556}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}}} \]

      4. associate-/l* 92.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   10. Simplified 92.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{0.005555555555555556}}}} \]

   11. Taylor expanded in A around 0 84.4%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{0.005555555555555556}}} \]
   12. Step-by-step derivation

       1. unpow2 84.4%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{0.005555555555555556}}} \]

       2. unpow2 84.4%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{0.005555555555555556}}} \]

       3. hypot-def 90.8%

          \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   13. Simplified 90.8%

       \[\leadsto \frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{0.005555555555555556}}} \]

   if -1.3999999999999999e-17 < C < 2.0499999999999999e99

   1. Initial program 57.3%

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

   4. Applied egg-rr 85.9%

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

      1. associate-/r* 86.0%

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

      2. associate--l- 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in C around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. unpow2 56.0%

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

      4. unpow2 56.0%

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

      5. hypot-def 84.6%

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

   9. Simplified 84.6%

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

       1. expm1-log1p-u 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)\right)} \]

       2. expm1-udef 47.2%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}}\right)} - 1} \]

       3. associate-/r/ 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{1}{\frac{\pi}{180}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}\right)} - 1 \]

       4. div-inv 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{\pi \cdot \frac{1}{180}}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       5. metadata-eval 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot \color{blue}{0.005555555555555556}} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\right)} - 1 \]

       6. distribute-frac-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}\right)} - 1 \]

       7. atan-neg 47.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}\right)} - 1 \]

   11. Applied egg-rr 47.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 47.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)\right)\right)} \]

       2. expm1-log1p 84.6%

          \[\leadsto \color{blue}{\frac{1}{\pi \cdot 0.005555555555555556} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)} \]

       3. associate-*l/ 84.6%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)\right)}{\pi \cdot 0.005555555555555556}} \]

       4. *-lft-identity 84.6%

          \[\leadsto \frac{\color{blue}{-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       5. neg-mul-1 84.6%

          \[\leadsto \frac{\color{blue}{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}}{\pi \cdot 0.005555555555555556} \]

       6. *-commutative 84.6%

          \[\leadsto \frac{-1 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       7. times-frac 84.6%

          \[\leadsto \color{blue}{\frac{-1}{0.005555555555555556} \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}} \]

       8. metadata-eval 84.6%

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

   13. Simplified 84.6%

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

   if 2.0499999999999999e99 < C

   1. Initial program 23.1%

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

   3. Taylor expanded in A around 0 23.1%

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

      1. unpow2 23.1%

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

      2. unpow2 23.1%

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

      3. hypot-def 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in C around inf 71.4%

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

   7. Taylor expanded in B around 0 76.8%

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

      1. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

   10. Taylor expanded in B around 0 76.8%

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

       1. associate-*r/ 76.8%

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

       2. associate-*l/ 76.9%

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

       3. metadata-eval 76.9%

          \[\leadsto \frac{\color{blue}{\frac{1}{0.005555555555555556}}}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       4. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \pi}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       5. *-commutative 76.9%

          \[\leadsto \frac{1}{\color{blue}{\pi \cdot 0.005555555555555556}} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \]

       6. *-commutative 76.9%

          \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{1}{\pi \cdot 0.005555555555555556}} \]

       7. associate-*r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5 \cdot B}{C}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       8. associate-/l* 77.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{\frac{C}{B}}\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       9. associate-/r/ 76.9%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-0.5}{C} \cdot B\right)} \cdot \frac{1}{\pi \cdot 0.005555555555555556} \]

       10. *-commutative 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \frac{1}{\color{blue}{0.005555555555555556 \cdot \pi}} \]

       11. associate-/r* 76.9%

           \[\leadsto \tan^{-1} \left(\frac{-0.5}{C} \cdot B\right) \cdot \color{blue}{\frac{\frac{1}{0.005555555555555556}}{\pi}} \]

       12. metadata-eval 76.9%

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

   12. Simplified 76.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 7.5 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{A - C} + \frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 7.5e-290)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 2.1e-36)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 8.6e+25)
       (* 180.0 (/ (atan (+ (* -0.5 (/ B (- A C))) (/ (* (- C A) 2.0) B))) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 7.5e-290) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 2.1e-36) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 8.6e+25) {
		tmp = 180.0 * (atan(((-0.5 * (B / (A - C))) + (((C - A) * 2.0) / 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 <= 7.5e-290) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 2.1e-36) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 8.6e+25) {
		tmp = 180.0 * (Math.atan(((-0.5 * (B / (A - C))) + (((C - A) * 2.0) / 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 <= 7.5e-290:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 2.1e-36:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 8.6e+25:
		tmp = 180.0 * (math.atan(((-0.5 * (B / (A - C))) + (((C - A) * 2.0) / 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 <= 7.5e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 2.1e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 8.6e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(B / Float64(A - C))) + Float64(Float64(Float64(C - A) * 2.0) / 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 <= 7.5e-290)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 2.1e-36)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 8.6e+25)
		tmp = 180.0 * (atan(((-0.5 * (B / (A - C))) + (((C - A) * 2.0) / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 7.5e-290], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-36], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.6e+25], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(B / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(C - A), $MachinePrecision] * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < 7.4999999999999995e-290

   1. Initial program 64.3%

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

   3. Taylor expanded in B around -inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. div-sub 73.0%

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

   5. Simplified 73.0%

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

   if 7.4999999999999995e-290 < B < 2.09999999999999991e-36

   1. Initial program 54.9%

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

   3. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. metadata-eval 55.2%

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

      4. mul0-lft 55.2%

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

      5. metadata-eval 55.2%

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

   5. Simplified 55.2%

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

   if 2.09999999999999991e-36 < B < 8.59999999999999996e25

   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 B around 0 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-*r/ 81.9%

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

      3. associate-*r/ 81.9%

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

      4. div-sub 81.9%

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

      5. distribute-lft-out-- 81.9%

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

   5. Simplified 81.9%

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

   if 8.59999999999999996e25 < B

   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 B around inf 63.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7.5 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{A - C} + \frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-182}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-293}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -2.5e-54)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -9.5e-182)
       t_0
       (if (<= B -9e-274)
         t_1
         (if (<= B -1.2e-293)
           t_0
           (if (<= B 1.35e-33) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.5e-54) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.5e-182) {
		tmp = t_0;
	} else if (B <= -9e-274) {
		tmp = t_1;
	} else if (B <= -1.2e-293) {
		tmp = t_0;
	} else if (B <= 1.35e-33) {
		tmp = t_1;
	} 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 * (A / B))) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -2.5e-54) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.5e-182) {
		tmp = t_0;
	} else if (B <= -9e-274) {
		tmp = t_1;
	} else if (B <= -1.2e-293) {
		tmp = t_0;
	} else if (B <= 1.35e-33) {
		tmp = t_1;
	} 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 * (A / B))) / math.pi)
	t_1 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -2.5e-54:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.5e-182:
		tmp = t_0
	elif B <= -9e-274:
		tmp = t_1
	elif B <= -1.2e-293:
		tmp = t_0
	elif B <= 1.35e-33:
		tmp = t_1
	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(A / B))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -2.5e-54)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.5e-182)
		tmp = t_0;
	elseif (B <= -9e-274)
		tmp = t_1;
	elseif (B <= -1.2e-293)
		tmp = t_0;
	elseif (B <= 1.35e-33)
		tmp = t_1;
	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 * (A / B))) / pi);
	t_1 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -2.5e-54)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.5e-182)
		tmp = t_0;
	elseif (B <= -9e-274)
		tmp = t_1;
	elseif (B <= -1.2e-293)
		tmp = t_0;
	elseif (B <= 1.35e-33)
		tmp = t_1;
	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[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.5e-54], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-182], t$95$0, If[LessEqual[B, -9e-274], t$95$1, If[LessEqual[B, -1.2e-293], t$95$0, If[LessEqual[B, 1.35e-33], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.50000000000000008e-54

   1. Initial program 59.1%

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

   3. Taylor expanded in B around -inf 58.0%

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

   if -2.50000000000000008e-54 < B < -9.4999999999999994e-182 or -8.99999999999999982e-274 < B < -1.2e-293

   1. Initial program 75.9%

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

   3. Taylor expanded in A around inf 61.2%

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

   if -9.4999999999999994e-182 < B < -8.99999999999999982e-274 or -1.2e-293 < B < 1.35e-33

   1. Initial program 59.0%

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

   3. Taylor expanded in C around inf 50.6%

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

      1. associate-*r/ 50.6%

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

      2. distribute-rgt1-in 50.6%

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

      3. metadata-eval 50.6%

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

      4. mul0-lft 50.6%

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

      5. metadata-eval 50.6%

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

   5. Simplified 50.6%

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

   if 1.35e-33 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -4.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ B C) B)) PI))))
   (if (<= B -8.5e-55)
     t_0
     (if (<= B -4.9e-163)
       (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
       (if (<= B 4.5e-291)
         t_0
         (if (<= B 2.2e-36)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	double tmp;
	if (B <= -8.5e-55) {
		tmp = t_0;
	} else if (B <= -4.9e-163) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 4.5e-291) {
		tmp = t_0;
	} else if (B <= 2.2e-36) {
		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 t_0 = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	double tmp;
	if (B <= -8.5e-55) {
		tmp = t_0;
	} else if (B <= -4.9e-163) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 4.5e-291) {
		tmp = t_0;
	} else if (B <= 2.2e-36) {
		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):
	t_0 = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	tmp = 0
	if B <= -8.5e-55:
		tmp = t_0
	elif B <= -4.9e-163:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 4.5e-291:
		tmp = t_0
	elif B <= 2.2e-36:
		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)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi))
	tmp = 0.0
	if (B <= -8.5e-55)
		tmp = t_0;
	elseif (B <= -4.9e-163)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 4.5e-291)
		tmp = t_0;
	elseif (B <= 2.2e-36)
		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)
	t_0 = 180.0 * (atan(((B + C) / B)) / pi);
	tmp = 0.0;
	if (B <= -8.5e-55)
		tmp = t_0;
	elseif (B <= -4.9e-163)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 4.5e-291)
		tmp = t_0;
	elseif (B <= 2.2e-36)
		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_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8.5e-55], t$95$0, If[LessEqual[B, -4.9e-163], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-291], t$95$0, If[LessEqual[B, 2.2e-36], 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 4 regimes

2. if B < -8.49999999999999968e-55 or -4.9000000000000003e-163 < B < 4.49999999999999974e-291

   1. Initial program 63.4%

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

   3. Taylor expanded in A around 0 58.4%

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

      1. unpow2 58.4%

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

      2. unpow2 58.4%

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

      3. hypot-def 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in B around -inf 68.3%

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

   if -8.49999999999999968e-55 < B < -4.9000000000000003e-163

   1. Initial program 69.8%

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

   3. Taylor expanded in A around inf 54.1%

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

   if 4.49999999999999974e-291 < B < 2.1999999999999999e-36

   1. Initial program 54.9%

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

   3. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. metadata-eval 55.2%

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

      4. mul0-lft 55.2%

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

      5. metadata-eval 55.2%

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

   5. Simplified 55.2%

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

   if 2.1999999999999999e-36 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.2e-15)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.1e-290)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 2.1e-36)
       (* 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 <= -8.2e-15) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.1e-290) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 2.1e-36) {
		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 <= -8.2e-15) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.1e-290) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 2.1e-36) {
		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 <= -8.2e-15:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.1e-290:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 2.1e-36:
		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 <= -8.2e-15)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.1e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 2.1e-36)
		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 <= -8.2e-15)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.1e-290)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 2.1e-36)
		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, -8.2e-15], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-290], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-36], 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 4 regimes

2. if B < -8.20000000000000072e-15

   1. Initial program 58.4%

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

   3. Taylor expanded in B around -inf 61.8%

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

   if -8.20000000000000072e-15 < B < 2.1000000000000001e-290

   1. Initial program 71.5%

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

   3. Taylor expanded in C around -inf 49.0%

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

   if 2.1000000000000001e-290 < B < 2.09999999999999991e-36

   1. Initial program 54.9%

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

   3. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. metadata-eval 55.2%

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

      4. mul0-lft 55.2%

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

      5. metadata-eval 55.2%

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

   5. Simplified 55.2%

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

   if 2.09999999999999991e-36 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.55e-43)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.5e-32)
     (* 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 <= -1.55e-43) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.5e-32) {
		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 <= -1.55e-43) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.5e-32) {
		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 <= -1.55e-43:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.5e-32:
		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 <= -1.55e-43)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.5e-32)
		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 <= -1.55e-43)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.5e-32)
		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, -1.55e-43], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-32], 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 < -1.55e-43

   1. Initial program 59.3%

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

   3. Taylor expanded in B around -inf 59.3%

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

   if -1.55e-43 < B < 6.49999999999999988e-32

   1. Initial program 63.8%

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

   3. Taylor expanded in C around inf 41.4%

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

      1. associate-*r/ 41.4%

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

      2. distribute-rgt1-in 41.4%

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

      3. metadata-eval 41.4%

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

      4. mul0-lft 41.4%

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

      5. metadata-eval 41.4%

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

   5. Simplified 41.4%

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

   if 6.49999999999999988e-32 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.2 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.2e-289)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 4e-36)
     (* 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 <= 3.2e-289) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 4e-36) {
		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 <= 3.2e-289) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 4e-36) {
		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 <= 3.2e-289:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 4e-36:
		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 <= 3.2e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 4e-36)
		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 <= 3.2e-289)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 4e-36)
		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, 3.2e-289], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-36], 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 < 3.2000000000000002e-289

   1. Initial program 64.3%

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

   3. Taylor expanded in B around -inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. div-sub 73.0%

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

   5. Simplified 73.0%

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

   if 3.2000000000000002e-289 < B < 3.9999999999999998e-36

   1. Initial program 54.9%

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

   3. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. metadata-eval 55.2%

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

      4. mul0-lft 55.2%

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

      5. metadata-eval 55.2%

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

   5. Simplified 55.2%

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

   if 3.9999999999999998e-36 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.2 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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, -5e-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 < -4.999999999999985e-310

   1. Initial program 63.9%

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

   3. Taylor expanded in B around -inf 40.3%

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

   if -4.999999999999985e-310 < B

   1. Initial program 55.4%

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

   3. Taylor expanded in B around inf 41.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.0% 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 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. Add Preprocessing

3. Taylor expanded in B around inf 22.3%

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

4. Final simplification 22.3%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))