ABCF->ab-angle angle

Percentage Accurate: 53.7% → 80.9%

Time: 22.7s

Alternatives: 17

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% 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: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.2e+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 <= -3.2e+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 <= -3.2e+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 <= -3.2e+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 <= -3.2e+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 <= -3.2e+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, -3.2e+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 < -3.2e165

   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 54.0%

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

      1. associate-/r* 54.0%

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

      2. associate--l- 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 87.3%

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

   if -3.2e165 < A

   1. Initial program 61.9%

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

      1. associate-*r/ 61.9%

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

      2. associate-*l/ 61.9%

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

      3. *-un-lft-identity 61.9%

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

      4. unpow2 61.9%

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

      5. unpow2 61.9%

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

      6. hypot-def 85.0%

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

   4. Applied egg-rr 85.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{+98}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.5e-17)
   (/ 1.0 (/ PI (/ (atan (/ (- C (hypot B C)) B)) 0.005555555555555556)))
   (if (<= C 3e+98)
     (/ 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 <= -1.5e-17) {
		tmp = 1.0 / (((double) M_PI) / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 3e+98) {
		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 <= -1.5e-17) {
		tmp = 1.0 / (Math.PI / (Math.atan(((C - Math.hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 3e+98) {
		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 <= -1.5e-17:
		tmp = 1.0 / (math.pi / (math.atan(((C - math.hypot(B, C)) / B)) / 0.005555555555555556))
	elif C <= 3e+98:
		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 <= -1.5e-17)
		tmp = Float64(1.0 / Float64(pi / Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / 0.005555555555555556)));
	elseif (C <= 3e+98)
		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 <= -1.5e-17)
		tmp = 1.0 / (pi / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	elseif (C <= 3e+98)
		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, -1.5e-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, 3e+98], 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 < -1.50000000000000003e-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 93.8%

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

      1. associate-/r* 93.8%

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

      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 90.9%

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

   13. Simplified 90.9%

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

   if -1.50000000000000003e-17 < C < 3.0000000000000001e98

   1. Initial program 52.2%

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

   4. Applied egg-rr 80.2%

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

      1. associate-/r* 80.2%

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

      2. associate--l- 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in C around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. +-commutative 51.6%

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

      3. unpow2 51.6%

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

      4. unpow2 51.6%

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

      5. hypot-def 79.6%

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

   9. Simplified 79.6%

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

   if 3.0000000000000001e98 < C

   1. Initial program 21.0%

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

   3. Taylor expanded in A around 0 21.0%

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

      1. unpow2 21.0%

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

      2. unpow2 21.0%

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

      3. hypot-def 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in C around inf 70.5%

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

   7. Taylor expanded in B around 0 81.8%

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

      1. associate-*r/ 81.9%

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

   9. Simplified 81.9%

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

   10. Taylor expanded in B around 0 81.8%

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

       1. associate-*r/ 81.9%

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

       2. associate-*l/ 82.0%

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

       3. metadata-eval 82.0%

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

       4. associate-/r* 82.0%

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

       5. *-commutative 82.0%

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

       6. *-commutative 82.0%

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

       7. associate-*r/ 82.0%

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

       8. associate-/l* 81.2%

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

       9. associate-/r/ 82.1%

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

       10. *-commutative 82.1%

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

       11. associate-/r* 82.1%

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

       12. metadata-eval 82.1%

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

   12. Simplified 82.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{+98}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.56 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{+101}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.56e-17)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= C 2.75e+101)
     (* -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 <= 2.75e+101) {
		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 <= 2.75e+101) {
		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 <= 2.75e+101:
		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 <= 2.75e+101)
		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 <= 2.75e+101)
		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, 2.75e+101], 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 < 2.75000000000000009e101

   1. Initial program 52.2%

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

   4. Applied egg-rr 80.2%

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

      1. associate-/r* 80.2%

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

      2. associate--l- 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in C around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. +-commutative 51.6%

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

      3. unpow2 51.6%

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

      4. unpow2 51.6%

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

      5. hypot-def 79.6%

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

   9. Simplified 79.6%

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

       1. expm1-log1p-u 42.2%

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

       2. expm1-udef 42.2%

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

       3. associate-/r/ 42.2%

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

       4. div-inv 42.2%

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

       5. metadata-eval 42.2%

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

       6. distribute-frac-neg 42.2%

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

       7. atan-neg 42.2%

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

   11. Applied egg-rr 42.2%

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

       1. expm1-def 42.2%

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

       2. expm1-log1p 79.6%

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

       3. associate-*l/ 79.6%

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

       4. *-lft-identity 79.6%

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

       5. neg-mul-1 79.6%

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

       6. *-commutative 79.6%

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

       7. times-frac 79.6%

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

       8. metadata-eval 79.6%

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

   13. Simplified 79.6%

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

   if 2.75000000000000009e101 < C

   1. Initial program 21.0%

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

   3. Taylor expanded in A around 0 21.0%

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

      1. unpow2 21.0%

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

      2. unpow2 21.0%

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

      3. hypot-def 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in C around inf 70.5%

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

   7. Taylor expanded in B around 0 81.8%

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

      1. associate-*r/ 81.9%

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

   9. Simplified 81.9%

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

   10. Taylor expanded in B around 0 81.8%

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

       1. associate-*r/ 81.9%

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

       2. associate-*l/ 82.0%

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

       3. metadata-eval 82.0%

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

       4. associate-/r* 82.0%

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

       5. *-commutative 82.0%

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

       6. *-commutative 82.0%

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

       7. associate-*r/ 82.0%

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

       8. associate-/l* 81.2%

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

       9. associate-/r/ 82.1%

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

       10. *-commutative 82.1%

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

       11. associate-/r* 82.1%

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

       12. metadata-eval 82.1%

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

   12. Simplified 82.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.56 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{+101}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.5e-17)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 1.1e+110)
     (* -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 <= -1.5e-17) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 1.1e+110) {
		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 <= -1.5e-17) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 1.1e+110) {
		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 <= -1.5e-17:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 1.1e+110:
		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 <= -1.5e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 1.1e+110)
		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 <= -1.5e-17)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 1.1e+110)
		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, -1.5e-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, 1.1e+110], 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 < -1.50000000000000003e-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 -1.50000000000000003e-17 < C < 1.09999999999999996e110

   1. Initial program 52.2%

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

   4. Applied egg-rr 80.2%

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

      1. associate-/r* 80.2%

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

      2. associate--l- 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in C around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. +-commutative 51.6%

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

      3. unpow2 51.6%

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

      4. unpow2 51.6%

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

      5. hypot-def 79.6%

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

   9. Simplified 79.6%

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

       1. expm1-log1p-u 42.2%

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

       2. expm1-udef 42.2%

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

       3. associate-/r/ 42.2%

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

       4. div-inv 42.2%

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

       5. metadata-eval 42.2%

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

       6. distribute-frac-neg 42.2%

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

       7. atan-neg 42.2%

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

   11. Applied egg-rr 42.2%

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

       1. expm1-def 42.2%

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

       2. expm1-log1p 79.6%

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

       3. associate-*l/ 79.6%

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

       4. *-lft-identity 79.6%

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

       5. neg-mul-1 79.6%

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

       6. *-commutative 79.6%

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

       7. times-frac 79.6%

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

       8. metadata-eval 79.6%

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

   13. Simplified 79.6%

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

   if 1.09999999999999996e110 < C

   1. Initial program 21.0%

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

   3. Taylor expanded in A around 0 21.0%

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

      1. unpow2 21.0%

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

      2. unpow2 21.0%

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

      3. hypot-def 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in C around inf 70.5%

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

   7. Taylor expanded in B around 0 81.8%

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

      1. associate-*r/ 81.9%

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

   9. Simplified 81.9%

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

   10. Taylor expanded in B around 0 81.8%

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

       1. associate-*r/ 81.9%

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

       2. associate-*l/ 82.0%

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

       3. metadata-eval 82.0%

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

       4. associate-/r* 82.0%

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

       5. *-commutative 82.0%

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

       6. *-commutative 82.0%

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

       7. associate-*r/ 82.0%

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

       8. associate-/l* 81.2%

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

       9. associate-/r/ 82.1%

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

       10. *-commutative 82.1%

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

       11. associate-/r* 82.1%

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

       12. metadata-eval 82.1%

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

   12. Simplified 82.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 2.25 \cdot 10^{+105}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.5e-17)
   (/ 1.0 (/ PI (/ (atan (/ (- C (hypot B C)) B)) 0.005555555555555556)))
   (if (<= C 2.25e+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 <= -1.5e-17) {
		tmp = 1.0 / (((double) M_PI) / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 2.25e+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 <= -1.5e-17) {
		tmp = 1.0 / (Math.PI / (Math.atan(((C - Math.hypot(B, C)) / B)) / 0.005555555555555556));
	} else if (C <= 2.25e+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 <= -1.5e-17:
		tmp = 1.0 / (math.pi / (math.atan(((C - math.hypot(B, C)) / B)) / 0.005555555555555556))
	elif C <= 2.25e+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 <= -1.5e-17)
		tmp = Float64(1.0 / Float64(pi / Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / 0.005555555555555556)));
	elseif (C <= 2.25e+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 <= -1.5e-17)
		tmp = 1.0 / (pi / (atan(((C - hypot(B, C)) / B)) / 0.005555555555555556));
	elseif (C <= 2.25e+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, -1.5e-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, 2.25e+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 < -1.50000000000000003e-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 93.8%

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

      1. associate-/r* 93.8%

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

      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 90.9%

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

   13. Simplified 90.9%

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

   if -1.50000000000000003e-17 < C < 2.2500000000000001e105

   1. Initial program 52.2%

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

   4. Applied egg-rr 80.2%

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

      1. associate-/r* 80.2%

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

      2. associate--l- 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in C around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. +-commutative 51.6%

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

      3. unpow2 51.6%

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

      4. unpow2 51.6%

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

      5. hypot-def 79.6%

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

   9. Simplified 79.6%

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

       1. expm1-log1p-u 42.2%

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

       2. expm1-udef 42.2%

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

       3. associate-/r/ 42.2%

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

       4. div-inv 42.2%

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

       5. metadata-eval 42.2%

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

       6. distribute-frac-neg 42.2%

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

       7. atan-neg 42.2%

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

   11. Applied egg-rr 42.2%

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

       1. expm1-def 42.2%

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

       2. expm1-log1p 79.6%

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

       3. associate-*l/ 79.6%

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

       4. *-lft-identity 79.6%

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

       5. neg-mul-1 79.6%

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

       6. *-commutative 79.6%

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

       7. times-frac 79.6%

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

       8. metadata-eval 79.6%

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

   13. Simplified 79.6%

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

   if 2.2500000000000001e105 < C

   1. Initial program 21.0%

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

   3. Taylor expanded in A around 0 21.0%

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

      1. unpow2 21.0%

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

      2. unpow2 21.0%

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

      3. hypot-def 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in C around inf 70.5%

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

   7. Taylor expanded in B around 0 81.8%

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

      1. associate-*r/ 81.9%

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

   9. Simplified 81.9%

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

   10. Taylor expanded in B around 0 81.8%

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

       1. associate-*r/ 81.9%

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

       2. associate-*l/ 82.0%

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

       3. metadata-eval 82.0%

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

       4. associate-/r* 82.0%

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

       5. *-commutative 82.0%

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

       6. *-commutative 82.0%

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

       7. associate-*r/ 82.0%

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

       8. associate-/l* 81.2%

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

       9. associate-/r/ 82.1%

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

       10. *-commutative 82.1%

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

       11. associate-/r* 82.1%

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

       12. metadata-eval 82.1%

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

   12. Simplified 82.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{0.005555555555555556}}}\\ \mathbf{elif}\;C \leq 2.25 \cdot 10^{+105}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+159}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.1e+159)
   (/ 1.0 (/ (/ PI 180.0) (atan (* 0.5 (/ B A)))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+159) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((0.5 * (B / A))));
	} 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 <= -1.1e+159) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((0.5 * (B / A))));
	} 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 <= -1.1e+159:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((0.5 * (B / A))))
	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 <= -1.1e+159)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(0.5 * Float64(B / A)))));
	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 <= -1.1e+159)
		tmp = 1.0 / ((pi / 180.0) / atan((0.5 * (B / A))));
	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, -1.1e+159], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.1e159

   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 54.0%

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

      1. associate-/r* 54.0%

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

      2. associate--l- 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 87.3%

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

   if -1.1e159 < A

   1. Initial program 61.9%

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

   3. Simplified 83.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+159}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq 1.7 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{A - C} + \frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B 1.7e-289)
     t_0
     (if (<= B 3.9e-163)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.5e-129)
         t_0
         (if (<= B 1.1e-35)
           (* (atan (* B (/ -0.5 C))) (/ 180.0 PI))
           (if (<= B 6e+28)
             (*
              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 t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= 1.7e-289) {
		tmp = t_0;
	} else if (B <= 3.9e-163) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.5e-129) {
		tmp = t_0;
	} else if (B <= 1.1e-35) {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	} else if (B <= 6e+28) {
		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 t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= 1.7e-289) {
		tmp = t_0;
	} else if (B <= 3.9e-163) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.5e-129) {
		tmp = t_0;
	} else if (B <= 1.1e-35) {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	} else if (B <= 6e+28) {
		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):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= 1.7e-289:
		tmp = t_0
	elif B <= 3.9e-163:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.5e-129:
		tmp = t_0
	elif B <= 1.1e-35:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	elif B <= 6e+28:
		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)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= 1.7e-289)
		tmp = t_0;
	elseif (B <= 3.9e-163)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.5e-129)
		tmp = t_0;
	elseif (B <= 1.1e-35)
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	elseif (B <= 6e+28)
		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)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= 1.7e-289)
		tmp = t_0;
	elseif (B <= 3.9e-163)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.5e-129)
		tmp = t_0;
	elseif (B <= 1.1e-35)
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	elseif (B <= 6e+28)
		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_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 1.7e-289], t$95$0, If[LessEqual[B, 3.9e-163], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.5e-129], t$95$0, If[LessEqual[B, 1.1e-35], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6e+28], 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 5 regimes

2. if B < 1.70000000000000009e-289 or 3.9000000000000002e-163 < B < 1.4999999999999999e-129

   1. Initial program 62.1%

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

   3. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 72.4%

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

   5. Simplified 72.4%

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

   if 1.70000000000000009e-289 < B < 3.9000000000000002e-163

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. distribute-rgt1-in 62.4%

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

      3. metadata-eval 62.4%

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

      4. mul0-lft 62.4%

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

      5. metadata-eval 62.4%

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

   5. Simplified 62.4%

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

   if 1.4999999999999999e-129 < B < 1.09999999999999997e-35

   1. Initial program 30.5%

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

   3. Taylor expanded in A around 0 35.9%

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

      1. unpow2 35.9%

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

      2. unpow2 35.9%

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

      3. hypot-def 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in C around inf 52.3%

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

   7. Taylor expanded in B around 0 51.8%

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

      1. associate-*r/ 51.6%

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

   9. Simplified 51.6%

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

   10. Taylor expanded in B around 0 51.8%

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

       1. associate-*r/ 51.6%

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

       2. associate-*l/ 51.8%

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

       3. metadata-eval 51.8%

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

       4. associate-/r* 51.8%

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

       5. *-commutative 51.8%

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

       6. *-commutative 51.8%

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

       7. associate-*r/ 51.8%

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

       8. associate-/l* 52.0%

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

       9. associate-/r/ 52.0%

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

       10. *-commutative 52.0%

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

       11. associate-/r* 52.0%

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

       12. metadata-eval 52.0%

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

   12. Simplified 52.0%

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

   if 1.09999999999999997e-35 < B < 6.0000000000000002e28

   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 6.0000000000000002e28 < 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 5 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.7 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{A - C} + \frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq 2 \cdot 10^{-291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) \cdot 2}{B} + 0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B 2e-291)
     t_0
     (if (<= B 8.2e-163)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.7e-129)
         t_0
         (if (<= B 1.15e-29)
           (* (atan (* B (/ -0.5 C))) (/ 180.0 PI))
           (if (<= B 3.5e+31)
             (/ (* 180.0 (atan (+ (/ (* (- C A) 2.0) B) (* 0.5 (/ B C))))) PI)
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= 2e-291) {
		tmp = t_0;
	} else if (B <= 8.2e-163) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.7e-129) {
		tmp = t_0;
	} else if (B <= 1.15e-29) {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	} else if (B <= 3.5e+31) {
		tmp = (180.0 * atan(((((C - A) * 2.0) / B) + (0.5 * (B / C))))) / ((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((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= 2e-291) {
		tmp = t_0;
	} else if (B <= 8.2e-163) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.7e-129) {
		tmp = t_0;
	} else if (B <= 1.15e-29) {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	} else if (B <= 3.5e+31) {
		tmp = (180.0 * Math.atan(((((C - A) * 2.0) / B) + (0.5 * (B / C))))) / 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((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= 2e-291:
		tmp = t_0
	elif B <= 8.2e-163:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.7e-129:
		tmp = t_0
	elif B <= 1.15e-29:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	elif B <= 3.5e+31:
		tmp = (180.0 * math.atan(((((C - A) * 2.0) / B) + (0.5 * (B / C))))) / 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(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= 2e-291)
		tmp = t_0;
	elseif (B <= 8.2e-163)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.7e-129)
		tmp = t_0;
	elseif (B <= 1.15e-29)
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	elseif (B <= 3.5e+31)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(Float64(C - A) * 2.0) / B) + Float64(0.5 * Float64(B / C))))) / 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((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= 2e-291)
		tmp = t_0;
	elseif (B <= 8.2e-163)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.7e-129)
		tmp = t_0;
	elseif (B <= 1.15e-29)
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	elseif (B <= 3.5e+31)
		tmp = (180.0 * atan(((((C - A) * 2.0) / B) + (0.5 * (B / C))))) / 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[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 2e-291], t$95$0, If[LessEqual[B, 8.2e-163], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-129], t$95$0, If[LessEqual[B, 1.15e-29], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e+31], N[(N[(180.0 * N[ArcTan[N[(N[(N[(N[(C - A), $MachinePrecision] * 2.0), $MachinePrecision] / B), $MachinePrecision] + N[(0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < 1.99999999999999992e-291 or 8.19999999999999965e-163 < B < 1.70000000000000007e-129

   1. Initial program 62.1%

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

   3. Taylor expanded in B around -inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. div-sub 72.4%

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

   5. Simplified 72.4%

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

   if 1.99999999999999992e-291 < B < 8.19999999999999965e-163

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. distribute-rgt1-in 62.4%

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

      3. metadata-eval 62.4%

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

      4. mul0-lft 62.4%

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

      5. metadata-eval 62.4%

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

   5. Simplified 62.4%

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

   if 1.70000000000000007e-129 < B < 1.14999999999999996e-29

   1. Initial program 30.5%

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

   3. Taylor expanded in A around 0 35.9%

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

      1. unpow2 35.9%

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

      2. unpow2 35.9%

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

      3. hypot-def 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in C around inf 52.3%

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

   7. Taylor expanded in B around 0 51.8%

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

      1. associate-*r/ 51.6%

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

   9. Simplified 51.6%

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

   10. Taylor expanded in B around 0 51.8%

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

       1. associate-*r/ 51.6%

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

       2. associate-*l/ 51.8%

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

       3. metadata-eval 51.8%

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

       4. associate-/r* 51.8%

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

       5. *-commutative 51.8%

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

       6. *-commutative 51.8%

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

       7. associate-*r/ 51.8%

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

       8. associate-/l* 52.0%

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

       9. associate-/r/ 52.0%

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

       10. *-commutative 52.0%

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

       11. associate-/r* 52.0%

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

       12. metadata-eval 52.0%

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

   12. Simplified 52.0%

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

   if 1.14999999999999996e-29 < B < 3.5e31

   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. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. unpow2 100.0%

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

      5. unpow2 100.0%

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

      6. hypot-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in C around -inf 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-+r+ 80.0%

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

      3. +-commutative 80.0%

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

      4. metadata-eval 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. associate-*r/ 80.0%

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

      7. associate-*r/ 80.0%

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

      8. div-sub 80.0%

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

      9. distribute-lft-out-- 80.0%

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

   7. Simplified 80.0%

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

   if 3.5e31 < 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 5 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) \cdot 2}{B} + 0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq 3.8 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-34}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B 3.8e-289)
     t_0
     (if (<= B 3.9e-163)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.7e-129)
         t_0
         (if (<= B 1.2e-34)
           (* (atan (* B (/ -0.5 C))) (/ 180.0 PI))
           (if (<= B 1.1e+30) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= 3.8e-289) {
		tmp = t_0;
	} else if (B <= 3.9e-163) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.7e-129) {
		tmp = t_0;
	} else if (B <= 1.2e-34) {
		tmp = atan((B * (-0.5 / C))) * (180.0 / ((double) M_PI));
	} else if (B <= 1.1e+30) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= 3.8e-289) {
		tmp = t_0;
	} else if (B <= 3.9e-163) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.7e-129) {
		tmp = t_0;
	} else if (B <= 1.2e-34) {
		tmp = Math.atan((B * (-0.5 / C))) * (180.0 / Math.PI);
	} else if (B <= 1.1e+30) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= 3.8e-289:
		tmp = t_0
	elif B <= 3.9e-163:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.7e-129:
		tmp = t_0
	elif B <= 1.2e-34:
		tmp = math.atan((B * (-0.5 / C))) * (180.0 / math.pi)
	elif B <= 1.1e+30:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= 3.8e-289)
		tmp = t_0;
	elseif (B <= 3.9e-163)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.7e-129)
		tmp = t_0;
	elseif (B <= 1.2e-34)
		tmp = Float64(atan(Float64(B * Float64(-0.5 / C))) * Float64(180.0 / pi));
	elseif (B <= 1.1e+30)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= 3.8e-289)
		tmp = t_0;
	elseif (B <= 3.9e-163)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.7e-129)
		tmp = t_0;
	elseif (B <= 1.2e-34)
		tmp = atan((B * (-0.5 / C))) * (180.0 / pi);
	elseif (B <= 1.1e+30)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, 3.8e-289], t$95$0, If[LessEqual[B, 3.9e-163], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-129], t$95$0, If[LessEqual[B, 1.2e-34], N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e+30], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < 3.80000000000000009e-289 or 3.9000000000000002e-163 < B < 1.70000000000000007e-129 or 1.19999999999999996e-34 < B < 1.1e30

   1. Initial program 64.4%

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

   3. Taylor expanded in B around -inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. div-sub 72.8%

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

   5. Simplified 72.8%

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

   if 3.80000000000000009e-289 < B < 3.9000000000000002e-163

   1. Initial program 49.2%

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

   3. Taylor expanded in C around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. distribute-rgt1-in 62.4%

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

      3. metadata-eval 62.4%

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

      4. mul0-lft 62.4%

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

      5. metadata-eval 62.4%

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

   5. Simplified 62.4%

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

   if 1.70000000000000007e-129 < B < 1.19999999999999996e-34

   1. Initial program 30.5%

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

   3. Taylor expanded in A around 0 35.9%

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

      1. unpow2 35.9%

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

      2. unpow2 35.9%

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

      3. hypot-def 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in C around inf 52.3%

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

   7. Taylor expanded in B around 0 51.8%

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

      1. associate-*r/ 51.6%

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

   9. Simplified 51.6%

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

   10. Taylor expanded in B around 0 51.8%

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

       1. associate-*r/ 51.6%

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

       2. associate-*l/ 51.8%

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

       3. metadata-eval 51.8%

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

       4. associate-/r* 51.8%

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

       5. *-commutative 51.8%

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

       6. *-commutative 51.8%

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

       7. associate-*r/ 51.8%

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

       8. associate-/l* 52.0%

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

       9. associate-/r/ 52.0%

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

       10. *-commutative 52.0%

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

       11. associate-/r* 52.0%

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

       12. metadata-eval 52.0%

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

   12. Simplified 52.0%

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

   if 1.1e30 < 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 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.8 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-34}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.08 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.36e-17)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C -1.08e-134)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= C 2.2e-27)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.36e-17) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -1.08e-134) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 2.2e-27) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.36e-17) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -1.08e-134) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 2.2e-27) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.36e-17:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -1.08e-134:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 2.2e-27:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.36e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -1.08e-134)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 2.2e-27)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.36e-17)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -1.08e-134)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 2.2e-27)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.36e-17], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.08e-134], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.2e-27], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.36e-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 C around -inf 75.1%

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

   if -1.36e-17 < C < -1.07999999999999999e-134

   1. Initial program 64.5%

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

   3. Taylor expanded in B around -inf 42.0%

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

   if -1.07999999999999999e-134 < C < 2.19999999999999987e-27

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 37.9%

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

   if 2.19999999999999987e-27 < C

   1. Initial program 28.0%

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

   3. Taylor expanded in A around 0 24.2%

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

      1. unpow2 24.2%

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

      2. unpow2 24.2%

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

      3. hypot-def 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in C around inf 70.5%

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

      1. associate-*r/ 70.5%

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

   8. Simplified 70.5%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.08 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.4 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.4e-54)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.6e-289)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= B 2.05e-78)
       (* 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 <= -2.4e-54) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.6e-289) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 2.05e-78) {
		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 <= -2.4e-54) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.6e-289) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 2.05e-78) {
		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 <= -2.4e-54:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.6e-289:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 2.05e-78:
		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 <= -2.4e-54)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.6e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 2.05e-78)
		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 <= -2.4e-54)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.6e-289)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 2.05e-78)
		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, -2.4e-54], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-289], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.05e-78], 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 < -2.40000000000000013e-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 -2.40000000000000013e-54 < B < 3.6e-289

   1. Initial program 66.1%

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

   3. Taylor expanded in A around inf 44.6%

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

   if 3.6e-289 < B < 2.0499999999999999e-78

   1. Initial program 46.7%

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

   3. Taylor expanded in C around inf 48.3%

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

      1. associate-*r/ 48.3%

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

      2. distribute-rgt1-in 48.3%

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

      3. metadata-eval 48.3%

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

      4. mul0-lft 48.3%

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

      5. metadata-eval 48.3%

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

   5. Simplified 48.3%

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

   if 2.0499999999999999e-78 < B

   1. Initial program 52.9%

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

   3. Taylor expanded in B around inf 56.5%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.4 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.2e-23)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.12e-289)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 1.65e-78)
       (* 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 <= -6.2e-23) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.12e-289) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 1.65e-78) {
		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 <= -6.2e-23) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.12e-289) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 1.65e-78) {
		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 <= -6.2e-23:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.12e-289:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 1.65e-78:
		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 <= -6.2e-23)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.12e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 1.65e-78)
		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 <= -6.2e-23)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.12e-289)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 1.65e-78)
		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, -6.2e-23], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.12e-289], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.65e-78], 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 < -6.1999999999999998e-23

   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 -6.1999999999999998e-23 < B < 1.11999999999999999e-289

   1. Initial program 66.3%

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

   3. Taylor expanded in C around -inf 49.0%

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

   if 1.11999999999999999e-289 < B < 1.64999999999999991e-78

   1. Initial program 46.7%

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

   3. Taylor expanded in C around inf 48.3%

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

      1. associate-*r/ 48.3%

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

      2. distribute-rgt1-in 48.3%

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

      3. metadata-eval 48.3%

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

      4. mul0-lft 48.3%

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

      5. metadata-eval 48.3%

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

   5. Simplified 48.3%

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

   if 1.64999999999999991e-78 < B

   1. Initial program 52.9%

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

   3. Taylor expanded in B around inf 56.5%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.8e+39)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 4.2e+72)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.8e+39) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 4.2e+72) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.8e+39) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 4.2e+72) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.8e+39:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 4.2e+72:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.8e+39)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 4.2e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.8e+39)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 4.2e+72)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.8e+39], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.2e+72], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.8000000000000002e39

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

   5. Simplified 68.1%

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

   if -7.8000000000000002e39 < A < 4.2000000000000003e72

   1. Initial program 59.8%

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

   3. Taylor expanded in A around 0 57.1%

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

      1. unpow2 57.1%

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

      2. unpow2 57.1%

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

      3. hypot-def 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in B around -inf 52.4%

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

   if 4.2000000000000003e72 < A

   1. Initial program 80.5%

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

   3. Taylor expanded in A around inf 71.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e+40)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 2.2e+72)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+40) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 2.2e+72) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+40) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 2.2e+72) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e+40:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 2.2e+72:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e+40)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 2.2e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e+40)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 2.2e+72)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e+40], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.2e+72], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35000000000000005e40

   1. Initial program 26.7%

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

      1. associate-*r/ 26.7%

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

      2. associate-*l/ 26.7%

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

      3. *-un-lft-identity 26.7%

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

      4. unpow2 26.7%

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

      5. unpow2 26.7%

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

      6. hypot-def 60.9%

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

   4. Applied egg-rr 60.9%

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

   5. Taylor expanded in A around -inf 68.3%

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

   if -1.35000000000000005e40 < A < 2.2e72

   1. Initial program 59.8%

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

   3. Taylor expanded in A around 0 57.1%

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

      1. unpow2 57.1%

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

      2. unpow2 57.1%

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

      3. hypot-def 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in B around -inf 52.4%

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

   if 2.2e72 < A

   1. Initial program 80.5%

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

   3. Taylor expanded in A around inf 71.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.6e-76)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.15e-78)
     (* 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 <= -6.6e-76) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.15e-78) {
		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 <= -6.6e-76) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.15e-78) {
		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 <= -6.6e-76:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.15e-78:
		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 <= -6.6e-76)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.15e-78)
		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 <= -6.6e-76)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.15e-78)
		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, -6.6e-76], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.15e-78], 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 < -6.59999999999999967e-76

   1. Initial program 60.4%

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

   3. Taylor expanded in B around -inf 55.4%

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

   if -6.59999999999999967e-76 < B < 2.14999999999999997e-78

   1. Initial program 56.6%

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

   3. Taylor expanded in C around inf 35.6%

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

      1. associate-*r/ 35.6%

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

      2. distribute-rgt1-in 35.6%

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

      3. metadata-eval 35.6%

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

      4. mul0-lft 35.6%

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

      5. metadata-eval 35.6%

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

   5. Simplified 35.6%

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

   if 2.14999999999999997e-78 < B

   1. Initial program 52.9%

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

   3. Taylor expanded in B around inf 56.5%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 61.5%

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

   3. Taylor expanded in B around -inf 40.4%

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

   if -4.999999999999985e-310 < B

   1. Initial program 51.8%

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

   3. Taylor expanded in B around inf 41.6%

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

4. Final simplification 41.0%

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

Alternative 17: 21.1% 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 56.5%

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