ABCF->ab-angle angle

Percentage Accurate: 53.9% → 81.6%

Time: 21.2s

Alternatives: 30

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 4.4e+101)
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)
   (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.4e+101) {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.4e+101) {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 4.4e+101:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 4.4e+101)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 4.4e+101)
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 4.4e+101], 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], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 4.4000000000000001e101

   1. Initial program 56.3%

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

      1. associate-*r/ 56.3%

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

      2. associate-*l/ 56.3%

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

      3. *-un-lft-identity 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-define 83.2%

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

   4. Applied egg-rr 83.2%

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

   if 4.4000000000000001e101 < C

   1. Initial program 12.5%

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

   4. Applied egg-rr 41.9%

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

   5. Taylor expanded in C around inf 83.9%

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

      1. distribute-rgt1-in 83.9%

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

      2. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 83.9%

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

      9. distribute-lft-neg-in 83.9%

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

      10. metadata-eval 83.9%

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

      11. associate-*r/ 83.9%

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

      12. *-commutative 83.9%

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

      13. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in B around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. associate-*r/ 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-*r/ 83.7%

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

      5. associate-*l/ 84.0%

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

   10. Simplified 84.0%

       \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 77.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(B, A\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 5.2e-34)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (* (+ A (hypot B A)) (/ -1.0 B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 5.2e-34) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) * (-1.0 / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 5.2e-34) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) * (-1.0 / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 5.2e-34:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) * (-1.0 / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 5.2e-34)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) * Float64(-1.0 / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 5.2e-34)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) * (-1.0 / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.2e-34], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A < 5.1999999999999999e-34

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 5.1999999999999999e-34 < A

   1. Initial program 77.7%

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

   3. Taylor expanded in C around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. +-commutative 72.9%

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

      3. unpow2 72.9%

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

      4. unpow2 72.9%

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

      5. hypot-define 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(B, A\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 5e-27)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* 180.0 (atan (/ (+ A (hypot A B)) (- B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 5e-27) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((A + hypot(A, B)) / -B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 5e-27) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((A + Math.hypot(A, B)) / -B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 5e-27:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((A + math.hypot(A, B)) / -B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 5e-27)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(A + hypot(A, B)) / Float64(-B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 5e-27)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 * atan(((A + hypot(A, B)) / -B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e-27], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A < 5.0000000000000002e-27

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 5.0000000000000002e-27 < A

   1. Initial program 77.7%

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

      1. associate-*r/ 77.7%

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

      2. associate-*l/ 77.7%

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

      3. *-un-lft-identity 77.7%

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

      4. unpow2 77.7%

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

      5. unpow2 77.7%

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

      6. hypot-define 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in C around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-neg-frac2 72.9%

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

      3. unpow2 72.9%

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

      4. unpow2 72.9%

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

      5. hypot-define 87.5%

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

   7. Simplified 87.5%

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

Alternative 4: 77.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.16 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 1.16e-21)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ 180.0 (/ PI (atan (/ (+ A (hypot A B)) (- B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 1.16e-21) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((A + hypot(A, B)) / -B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 1.16e-21) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((A + Math.hypot(A, B)) / -B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 1.16e-21:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((A + math.hypot(A, B)) / -B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 1.16e-21)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(A + hypot(A, B)) / Float64(-B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 1.16e-21)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan(((A + hypot(A, B)) / -B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.16e-21], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A < 1.1600000000000001e-21

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 1.1600000000000001e-21 < A

   1. Initial program 77.7%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in C around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-neg-frac2 72.9%

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

      3. unpow2 72.9%

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

      4. unpow2 72.9%

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

      5. hypot-define 87.5%

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

   7. Simplified 87.4%

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

Alternative 5: 77.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 1.65e-36)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 1.65e-36) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 1.65e-36) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 1.65e-36:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 1.65e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 1.65e-36)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.65e-36], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A < 1.64999999999999995e-36

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 1.64999999999999995e-36 < A

   1. Initial program 77.7%

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

   3. Taylor expanded in C around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-neg-frac2 72.9%

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

      3. +-commutative 72.9%

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

      4. unpow2 72.9%

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

      5. unpow2 72.9%

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

      6. hypot-define 87.4%

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

   5. Simplified 87.4%

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

Alternative 6: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (if (<= A 9.6e-16)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} else if (A <= 9.6e-16) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} else if (A <= 9.6e-16) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	elif A <= 9.6e-16:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	elseif (A <= 9.6e-16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	elseif (A <= 9.6e-16)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 9.6e-16], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A < 9.60000000000000019e-16

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 9.60000000000000019e-16 < A

   1. Initial program 77.7%

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

   3. Taylor expanded in B around -inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. div-sub 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 5.8e+100)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 5.8e+100) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 5.8e+100) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 5.8e+100:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 5.8e+100)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 5.8e+100)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 5.8e+100], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 5.8000000000000001e100

   1. Initial program 56.3%

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

      1. associate-*l/ 56.3%

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

      2. *-lft-identity 56.3%

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

      3. +-commutative 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-define 83.1%

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

   3. Simplified 83.1%

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

   if 5.8000000000000001e100 < C

   1. Initial program 12.5%

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

   4. Applied egg-rr 41.9%

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

   5. Taylor expanded in C around inf 83.9%

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

      1. distribute-rgt1-in 83.9%

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

      2. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 83.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 83.9%

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

      9. distribute-lft-neg-in 83.9%

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

      10. metadata-eval 83.9%

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

      11. associate-*r/ 83.9%

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

      12. *-commutative 83.9%

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

      13. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in B around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. associate-*r/ 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-*r/ 83.7%

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

      5. associate-*l/ 84.0%

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

   10. Simplified 84.0%

       \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 79.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-37)
   (/ (* 180.0 (atan (/ (* 0.5 (+ B (* B (/ C A)))) A))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-37) {
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / ((double) M_PI);
	} 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 <= -1.9e-37) {
		tmp = (180.0 * Math.atan(((0.5 * (B + (B * (C / A)))) / A))) / Math.PI;
	} 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 <= -1.9e-37:
		tmp = (180.0 * math.atan(((0.5 * (B + (B * (C / A)))) / A))) / math.pi
	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 <= -1.9e-37)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi);
	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 <= -1.9e-37)
		tmp = (180.0 * atan(((0.5 * (B + (B * (C / A)))) / A))) / pi;
	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, -1.9e-37], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -1.9000000000000002e-37

   1. Initial program 22.2%

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

      1. associate-*r/ 22.2%

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

      2. associate-*l/ 22.2%

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

      3. *-un-lft-identity 22.2%

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

      4. unpow2 22.2%

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

      5. unpow2 22.2%

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

      6. hypot-define 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. distribute-lft-out 68.1%

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

      3. associate-*r* 68.1%

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

      4. metadata-eval 68.1%

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

      5. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.9000000000000002e-37 < A

   1. Initial program 61.2%

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

   3. Simplified 85.0%

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

Alternative 9: 47.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-215}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -2.1e-18)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3e-215)
       t_0
       (if (<= B 1.7e-185)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= B 3.9e-41)
           (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
           (if (<= B 3.8e-23) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (B <= -2.1e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3e-215) {
		tmp = t_0;
	} else if (B <= 1.7e-185) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 3.9e-41) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 3.8e-23) {
		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((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (B <= -2.1e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3e-215) {
		tmp = t_0;
	} else if (B <= 1.7e-185) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 3.9e-41) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 3.8e-23) {
		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((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if B <= -2.1e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3e-215:
		tmp = t_0
	elif B <= 1.7e-185:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 3.9e-41:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 3.8e-23:
		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(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (B <= -2.1e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3e-215)
		tmp = t_0;
	elseif (B <= 1.7e-185)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 3.9e-41)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 3.8e-23)
		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((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (B <= -2.1e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3e-215)
		tmp = t_0;
	elseif (B <= 1.7e-185)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 3.9e-41)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 3.8e-23)
		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[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.1e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3e-215], t$95$0, If[LessEqual[B, 1.7e-185], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.9e-41], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-23], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.1e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -2.1e-18 < B < -3.00000000000000025e-215 or 3.89999999999999991e-41 < B < 3.80000000000000011e-23

   1. Initial program 36.4%

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

   3. Taylor expanded in C around inf 50.6%

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

   4. Taylor expanded in A around inf 50.6%

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

   if -3.00000000000000025e-215 < B < 1.6999999999999999e-185

   1. Initial program 65.3%

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

   3. Taylor expanded in A around inf 51.5%

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

   if 1.6999999999999999e-185 < B < 3.89999999999999991e-41

   1. Initial program 56.2%

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

   3. Taylor expanded in C around -inf 39.7%

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

   if 3.80000000000000011e-23 < B

   1. Initial program 54.3%

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

   3. Taylor expanded in B around inf 60.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.1 \cdot 10^{-218}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))))
   (if (<= B -3e-18)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.1e-218)
       t_0
       (if (<= B 1.1e-227)
         t_1
         (if (<= B 3.8e-28)
           t_0
           (if (<= B 1.65e-17) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	double tmp;
	if (B <= -3e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.1e-218) {
		tmp = t_0;
	} else if (B <= 1.1e-227) {
		tmp = t_1;
	} else if (B <= 3.8e-28) {
		tmp = t_0;
	} else if (B <= 1.65e-17) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	double tmp;
	if (B <= -3e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.1e-218) {
		tmp = t_0;
	} else if (B <= 1.1e-227) {
		tmp = t_1;
	} else if (B <= 3.8e-28) {
		tmp = t_0;
	} else if (B <= 1.65e-17) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	t_1 = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	tmp = 0
	if B <= -3e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.1e-218:
		tmp = t_0
	elif B <= 1.1e-227:
		tmp = t_1
	elif B <= 3.8e-28:
		tmp = t_0
	elif B <= 1.65e-17:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi))
	tmp = 0.0
	if (B <= -3e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.1e-218)
		tmp = t_0;
	elseif (B <= 1.1e-227)
		tmp = t_1;
	elseif (B <= 3.8e-28)
		tmp = t_0;
	elseif (B <= 1.65e-17)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	t_1 = 180.0 * (atan(((A / B) * -2.0)) / pi);
	tmp = 0.0;
	if (B <= -3e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.1e-218)
		tmp = t_0;
	elseif (B <= 1.1e-227)
		tmp = t_1;
	elseif (B <= 3.8e-28)
		tmp = t_0;
	elseif (B <= 1.65e-17)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.1e-218], t$95$0, If[LessEqual[B, 1.1e-227], t$95$1, If[LessEqual[B, 3.8e-28], t$95$0, If[LessEqual[B, 1.65e-17], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.99999999999999983e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -2.99999999999999983e-18 < B < -8.09999999999999988e-218 or 1.0999999999999999e-227 < B < 3.80000000000000009e-28

   1. Initial program 42.8%

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

   3. Taylor expanded in C around inf 40.4%

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

   4. Taylor expanded in A around inf 40.4%

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

   if -8.09999999999999988e-218 < B < 1.0999999999999999e-227 or 3.80000000000000009e-28 < B < 1.65e-17

   1. Initial program 71.4%

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

   3. Taylor expanded in A around inf 58.8%

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

   if 1.65e-17 < B

   1. Initial program 54.4%

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

   3. Taylor expanded in B around inf 61.5%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.1 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.72 \cdot 10^{-217}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{\frac{C}{A} + 1}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B -1.45e-31)
     (/ (* 180.0 (atan (- 1.0 t_0))) PI)
     (if (<= B -1.72e-217)
       (/ (* 180.0 (atan (* 0.5 (* B (/ (+ (/ C A) 1.0) A))))) PI)
       (if (<= B 7e-155)
         (/ (* 180.0 (atan (- -1.0 t_0))) PI)
         (if (<= B 2.5e-108)
           (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
           (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -1.45e-31) {
		tmp = (180.0 * atan((1.0 - t_0))) / ((double) M_PI);
	} else if (B <= -1.72e-217) {
		tmp = (180.0 * atan((0.5 * (B * (((C / A) + 1.0) / A))))) / ((double) M_PI);
	} else if (B <= 7e-155) {
		tmp = (180.0 * atan((-1.0 - t_0))) / ((double) M_PI);
	} else if (B <= 2.5e-108) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -1.45e-31) {
		tmp = (180.0 * Math.atan((1.0 - t_0))) / Math.PI;
	} else if (B <= -1.72e-217) {
		tmp = (180.0 * Math.atan((0.5 * (B * (((C / A) + 1.0) / A))))) / Math.PI;
	} else if (B <= 7e-155) {
		tmp = (180.0 * Math.atan((-1.0 - t_0))) / Math.PI;
	} else if (B <= 2.5e-108) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= -1.45e-31:
		tmp = (180.0 * math.atan((1.0 - t_0))) / math.pi
	elif B <= -1.72e-217:
		tmp = (180.0 * math.atan((0.5 * (B * (((C / A) + 1.0) / A))))) / math.pi
	elif B <= 7e-155:
		tmp = (180.0 * math.atan((-1.0 - t_0))) / math.pi
	elif B <= 2.5e-108:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= -1.45e-31)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - t_0))) / pi);
	elseif (B <= -1.72e-217)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B * Float64(Float64(Float64(C / A) + 1.0) / A))))) / pi);
	elseif (B <= 7e-155)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - t_0))) / pi);
	elseif (B <= 2.5e-108)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= -1.45e-31)
		tmp = (180.0 * atan((1.0 - t_0))) / pi;
	elseif (B <= -1.72e-217)
		tmp = (180.0 * atan((0.5 * (B * (((C / A) + 1.0) / A))))) / pi;
	elseif (B <= 7e-155)
		tmp = (180.0 * atan((-1.0 - t_0))) / pi;
	elseif (B <= 2.5e-108)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.45e-31], N[(N[(180.0 * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -1.72e-217], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B * N[(N[(N[(C / A), $MachinePrecision] + 1.0), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7e-155], N[(N[(180.0 * N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.5e-108], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.45e-31

   1. Initial program 43.4%

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

      1. associate-*r/ 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-un-lft-identity 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-define 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in B around -inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. div-sub 81.5%

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

   7. Simplified 81.5%

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

   if -1.45e-31 < B < -1.72e-217

   1. Initial program 30.7%

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

      1. associate-*r/ 30.7%

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

      2. associate-*l/ 30.7%

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

      3. *-un-lft-identity 30.7%

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

      4. unpow2 30.7%

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

      5. unpow2 30.7%

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

      6. hypot-define 55.2%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in A around -inf 44.6%

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

      1. associate-*r/ 44.6%

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

      2. distribute-lft-out 44.6%

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

      3. associate-*r* 44.6%

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

      4. metadata-eval 44.6%

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

      5. associate-/l* 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in B around 0 44.9%

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

      1. associate-/l* 44.9%

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

   10. Simplified 44.9%

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

   if -1.72e-217 < B < 7.00000000000000031e-155

   1. Initial program 65.7%

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

      1. associate-*r/ 65.7%

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

      2. associate-*l/ 65.7%

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

      3. *-un-lft-identity 65.7%

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

      4. unpow2 65.7%

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

      5. unpow2 65.7%

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

      6. hypot-define 83.4%

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

   4. Applied egg-rr 83.4%

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

   5. Taylor expanded in B around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. associate--r+ 61.7%

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

      3. div-sub 61.9%

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

   7. Simplified 61.9%

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

   if 7.00000000000000031e-155 < B < 2.5e-108

   1. Initial program 33.6%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in A around -inf 80.3%

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

   if 2.5e-108 < B

   1. Initial program 56.1%

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

   3. Taylor expanded in B around inf 73.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.72 \cdot 10^{-217}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(B \cdot \frac{\frac{C}{A} + 1}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B -8.5e-32)
     (/ (* 180.0 (atan (- 1.0 t_0))) PI)
     (if (<= B -1.25e-217)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (if (<= B 6.8e-155)
         (/ (* 180.0 (atan (- -1.0 t_0))) PI)
         (if (<= B 1.9e-108)
           (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
           (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * atan((1.0 - t_0))) / ((double) M_PI);
	} else if (B <= -1.25e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 6.8e-155) {
		tmp = (180.0 * atan((-1.0 - t_0))) / ((double) M_PI);
	} else if (B <= 1.9e-108) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * Math.atan((1.0 - t_0))) / Math.PI;
	} else if (B <= -1.25e-217) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 6.8e-155) {
		tmp = (180.0 * Math.atan((-1.0 - t_0))) / Math.PI;
	} else if (B <= 1.9e-108) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= -8.5e-32:
		tmp = (180.0 * math.atan((1.0 - t_0))) / math.pi
	elif B <= -1.25e-217:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 6.8e-155:
		tmp = (180.0 * math.atan((-1.0 - t_0))) / math.pi
	elif B <= 1.9e-108:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - t_0))) / pi);
	elseif (B <= -1.25e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 6.8e-155)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - t_0))) / pi);
	elseif (B <= 1.9e-108)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = (180.0 * atan((1.0 - t_0))) / pi;
	elseif (B <= -1.25e-217)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 6.8e-155)
		tmp = (180.0 * atan((-1.0 - t_0))) / pi;
	elseif (B <= 1.9e-108)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -8.5e-32], N[(N[(180.0 * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -1.25e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.8e-155], N[(N[(180.0 * N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.9e-108], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

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

      1. associate-*r/ 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-un-lft-identity 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-define 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in B around -inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. div-sub 81.5%

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

   7. Simplified 81.5%

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

   if -8.5000000000000003e-32 < B < -1.2500000000000001e-217

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if -1.2500000000000001e-217 < B < 6.8e-155

   1. Initial program 65.7%

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

      1. associate-*r/ 65.7%

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

      2. associate-*l/ 65.7%

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

      3. *-un-lft-identity 65.7%

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

      4. unpow2 65.7%

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

      5. unpow2 65.7%

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

      6. hypot-define 83.4%

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

   4. Applied egg-rr 83.4%

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

   5. Taylor expanded in B around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. associate--r+ 61.7%

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

      3. div-sub 61.9%

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

   7. Simplified 61.9%

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

   if 6.8e-155 < B < 1.89999999999999987e-108

   1. Initial program 33.6%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in A around -inf 80.3%

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

   if 1.89999999999999987e-108 < B

   1. Initial program 56.1%

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

   3. Taylor expanded in B around inf 73.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-155} \lor \neg \left(B \leq 3.2 \cdot 10^{-108}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - t\_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B -8.5e-32)
     (/ (* 180.0 (atan (- 1.0 t_0))) PI)
     (if (<= B -8.8e-213)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (if (or (<= B 6.8e-155) (not (<= B 3.2e-108)))
         (* 180.0 (/ (atan (- -1.0 t_0)) PI))
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * atan((1.0 - t_0))) / ((double) M_PI);
	} else if (B <= -8.8e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if ((B <= 6.8e-155) || !(B <= 3.2e-108)) {
		tmp = 180.0 * (atan((-1.0 - t_0)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * Math.atan((1.0 - t_0))) / Math.PI;
	} else if (B <= -8.8e-213) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if ((B <= 6.8e-155) || !(B <= 3.2e-108)) {
		tmp = 180.0 * (Math.atan((-1.0 - t_0)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= -8.5e-32:
		tmp = (180.0 * math.atan((1.0 - t_0))) / math.pi
	elif B <= -8.8e-213:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif (B <= 6.8e-155) or not (B <= 3.2e-108):
		tmp = 180.0 * (math.atan((-1.0 - t_0)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - t_0))) / pi);
	elseif (B <= -8.8e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif ((B <= 6.8e-155) || !(B <= 3.2e-108))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - t_0)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = (180.0 * atan((1.0 - t_0))) / pi;
	elseif (B <= -8.8e-213)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif ((B <= 6.8e-155) || ~((B <= 3.2e-108)))
		tmp = 180.0 * (atan((-1.0 - t_0)) / pi);
	else
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -8.5e-32], N[(N[(180.0 * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -8.8e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 6.8e-155], N[Not[LessEqual[B, 3.2e-108]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

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

      1. associate-*r/ 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-un-lft-identity 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-define 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in B around -inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. div-sub 81.5%

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

   7. Simplified 81.5%

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

   if -8.5000000000000003e-32 < B < -8.80000000000000039e-213

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if -8.80000000000000039e-213 < B < 6.8e-155 or 3.2e-108 < B

   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. Step-by-step derivation

      1. +-commutative 59.8%

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

      2. unpow2 59.8%

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

      3. unpow2 59.8%

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

      4. hypot-undefine 79.8%

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

      5. sub-neg 79.8%

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

      6. distribute-lft-in 70.8%

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

      7. hypot-undefine 57.4%

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

      8. unpow2 57.4%

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

      9. unpow2 57.4%

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

      10. +-commutative 57.4%

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

      11. unpow2 57.4%

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

      12. unpow2 57.4%

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

      13. hypot-define 70.8%

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

   4. Applied egg-rr 70.8%

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

   5. Taylor expanded in B around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. associate--r+ 69.2%

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

      3. div-sub 69.2%

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

      4. sub-neg 69.2%

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

      5. metadata-eval 69.2%

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

   7. Simplified 69.2%

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

   if 6.8e-155 < B < 3.2e-108

   1. Initial program 33.6%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in A around -inf 80.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-155} \lor \neg \left(B \leq 3.2 \cdot 10^{-108}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq -5.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - t\_0\right)\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-156} \lor \neg \left(B \leq 5.8 \cdot 10^{-108}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - t\_0\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B -5.3e-31)
     (* (/ 180.0 PI) (atan (- 1.0 t_0)))
     (if (<= B -8.8e-213)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (if (or (<= B 8e-156) (not (<= B 5.8e-108)))
         (* 180.0 (/ (atan (- -1.0 t_0)) PI))
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -5.3e-31) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - t_0));
	} else if (B <= -8.8e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if ((B <= 8e-156) || !(B <= 5.8e-108)) {
		tmp = 180.0 * (atan((-1.0 - t_0)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -5.3e-31) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - t_0));
	} else if (B <= -8.8e-213) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if ((B <= 8e-156) || !(B <= 5.8e-108)) {
		tmp = 180.0 * (Math.atan((-1.0 - t_0)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= -5.3e-31:
		tmp = (180.0 / math.pi) * math.atan((1.0 - t_0))
	elif B <= -8.8e-213:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif (B <= 8e-156) or not (B <= 5.8e-108):
		tmp = 180.0 * (math.atan((-1.0 - t_0)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= -5.3e-31)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - t_0)));
	elseif (B <= -8.8e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif ((B <= 8e-156) || !(B <= 5.8e-108))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - t_0)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= -5.3e-31)
		tmp = (180.0 / pi) * atan((1.0 - t_0));
	elseif (B <= -8.8e-213)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif ((B <= 8e-156) || ~((B <= 5.8e-108)))
		tmp = 180.0 * (atan((-1.0 - t_0)) / pi);
	else
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -5.3e-31], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.8e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 8e-156], N[Not[LessEqual[B, 5.8e-108]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -5.3000000000000001e-31

   1. Initial program 43.4%

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

      1. associate-*r/ 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-un-lft-identity 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-define 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in B around -inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. div-sub 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in C around -inf 81.4%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-/l* 81.4%

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

      4. mul-1-neg 81.4%

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

      5. unsub-neg 81.4%

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

      6. mul-1-neg 81.4%

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

      7. sub-neg 81.4%

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

   10. Simplified 81.4%

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

   if -5.3000000000000001e-31 < B < -8.80000000000000039e-213

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if -8.80000000000000039e-213 < B < 8.00000000000000032e-156 or 5.8000000000000002e-108 < B

   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. Step-by-step derivation

      1. +-commutative 59.8%

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

      2. unpow2 59.8%

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

      3. unpow2 59.8%

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

      4. hypot-undefine 79.8%

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

      5. sub-neg 79.8%

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

      6. distribute-lft-in 70.8%

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

      7. hypot-undefine 57.4%

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

      8. unpow2 57.4%

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

      9. unpow2 57.4%

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

      10. +-commutative 57.4%

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

      11. unpow2 57.4%

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

      12. unpow2 57.4%

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

      13. hypot-define 70.8%

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

   4. Applied egg-rr 70.8%

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

   5. Taylor expanded in B around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. associate--r+ 69.2%

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

      3. div-sub 69.2%

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

      4. sub-neg 69.2%

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

      5. metadata-eval 69.2%

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

   7. Simplified 69.2%

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

   if 8.00000000000000032e-156 < B < 5.8000000000000002e-108

   1. Initial program 33.6%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in A around -inf 80.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-156} \lor \neg \left(B \leq 5.8 \cdot 10^{-108}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ t_1 := \tan^{-1} \left(-1 - t\_0\right)\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot t\_1}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{t\_1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)) (t_1 (atan (- -1.0 t_0))))
   (if (<= B -8.5e-32)
     (/ (* 180.0 (atan (- 1.0 t_0))) PI)
     (if (<= B -6.5e-213)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (if (<= B 2e-155)
         (/ (* 180.0 t_1) PI)
         (if (<= B 1.75e-108)
           (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
           (* 180.0 (/ t_1 PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double t_1 = atan((-1.0 - t_0));
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * atan((1.0 - t_0))) / ((double) M_PI);
	} else if (B <= -6.5e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 2e-155) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (B <= 1.75e-108) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double t_1 = Math.atan((-1.0 - t_0));
	double tmp;
	if (B <= -8.5e-32) {
		tmp = (180.0 * Math.atan((1.0 - t_0))) / Math.PI;
	} else if (B <= -6.5e-213) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 2e-155) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (B <= 1.75e-108) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (t_1 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	t_1 = math.atan((-1.0 - t_0))
	tmp = 0
	if B <= -8.5e-32:
		tmp = (180.0 * math.atan((1.0 - t_0))) / math.pi
	elif B <= -6.5e-213:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 2e-155:
		tmp = (180.0 * t_1) / math.pi
	elif B <= 1.75e-108:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (t_1 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	t_1 = atan(Float64(-1.0 - t_0))
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - t_0))) / pi);
	elseif (B <= -6.5e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 2e-155)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (B <= 1.75e-108)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(t_1 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	t_1 = atan((-1.0 - t_0));
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = (180.0 * atan((1.0 - t_0))) / pi;
	elseif (B <= -6.5e-213)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 2e-155)
		tmp = (180.0 * t_1) / pi;
	elseif (B <= 1.75e-108)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (t_1 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[B, -8.5e-32], N[(N[(180.0 * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -6.5e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e-155], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.75e-108], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

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

      1. associate-*r/ 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-un-lft-identity 43.3%

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

      4. unpow2 43.3%

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

      5. unpow2 43.3%

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

      6. hypot-define 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in B around -inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. div-sub 81.5%

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

   7. Simplified 81.5%

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

   if -8.5000000000000003e-32 < B < -6.5e-213

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if -6.5e-213 < B < 2.00000000000000003e-155

   1. Initial program 65.7%

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

      1. associate-*r/ 65.7%

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

      2. associate-*l/ 65.7%

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

      3. *-un-lft-identity 65.7%

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

      4. unpow2 65.7%

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

      5. unpow2 65.7%

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

      6. hypot-define 83.4%

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

   4. Applied egg-rr 83.4%

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

   5. Taylor expanded in B around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. associate--r+ 61.7%

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

      3. div-sub 61.9%

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

   7. Simplified 61.9%

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

   if 2.00000000000000003e-155 < B < 1.7499999999999999e-108

   1. Initial program 33.6%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in A around -inf 80.3%

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

   if 1.7499999999999999e-108 < B

   1. Initial program 56.1%

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

      1. +-commutative 56.1%

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

      2. unpow2 56.1%

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

      3. unpow2 56.1%

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

      4. hypot-undefine 77.6%

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

      5. sub-neg 77.6%

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

      6. distribute-lft-in 76.3%

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

      7. hypot-undefine 56.1%

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

      8. unpow2 56.1%

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

      9. unpow2 56.1%

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

      10. +-commutative 56.1%

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

      11. unpow2 56.1%

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

      12. unpow2 56.1%

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

      13. hypot-define 76.3%

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

   4. Applied egg-rr 76.3%

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

   5. Taylor expanded in B around inf 73.7%

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

      1. +-commutative 73.7%

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

      2. associate--r+ 73.7%

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

      3. div-sub 73.7%

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

      4. sub-neg 73.7%

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

      5. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-218}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-155} \lor \neg \left(B \leq 1.5 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A + B}{-B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.5e-17)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -9.2e-218)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (or (<= B 6.2e-155) (not (<= B 1.5e-47)))
       (/ 180.0 (/ PI (atan (/ (+ A B) (- B)))))
       (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-17) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.2e-218) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if ((B <= 6.2e-155) || !(B <= 1.5e-47)) {
		tmp = 180.0 / (((double) M_PI) / atan(((A + B) / -B)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-17) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.2e-218) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if ((B <= 6.2e-155) || !(B <= 1.5e-47)) {
		tmp = 180.0 / (Math.PI / Math.atan(((A + B) / -B)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.5e-17:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.2e-218:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif (B <= 6.2e-155) or not (B <= 1.5e-47):
		tmp = 180.0 / (math.pi / math.atan(((A + B) / -B)))
	else:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.5e-17)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.2e-218)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif ((B <= 6.2e-155) || !(B <= 1.5e-47))
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(A + B) / Float64(-B)))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.5e-17)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.2e-218)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif ((B <= 6.2e-155) || ~((B <= 1.5e-47)))
		tmp = 180.0 / (pi / atan(((A + B) / -B)));
	else
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.5e-17], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.2e-218], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 6.2e-155], N[Not[LessEqual[B, 1.5e-47]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.50000000000000003e-17

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -1.50000000000000003e-17 < B < -9.19999999999999979e-218

   1. Initial program 34.7%

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

   4. Applied egg-rr 57.7%

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

   5. Taylor expanded in C around inf 47.9%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 47.9%

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

      9. distribute-lft-neg-in 47.9%

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

      10. metadata-eval 47.9%

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

      11. associate-*r/ 47.9%

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

      12. *-commutative 47.9%

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

      13. associate-/l* 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in B around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. *-commutative 47.8%

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

      4. associate-*r/ 47.8%

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

      5. associate-*l/ 47.9%

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

   10. Simplified 47.9%

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

   if -9.19999999999999979e-218 < B < 6.2e-155 or 1.50000000000000008e-47 < B

   1. Initial program 59.3%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in C around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-neg-frac2 52.6%

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

      3. unpow2 52.6%

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

      4. unpow2 52.6%

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

      5. hypot-define 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in A around 0 61.6%

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

   if 6.2e-155 < B < 1.50000000000000008e-47

   1. Initial program 50.0%

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

   4. Applied egg-rr 64.5%

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

   5. Taylor expanded in A around -inf 58.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-218}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-155} \lor \neg \left(B \leq 1.5 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A + B}{-B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-227}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.9e-217)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (<= B 1.7e-227)
       (/ (* 180.0 (atan (/ (* A -2.0) B))) PI)
       (if (<= B 3.3e-21)
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.1e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.9e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 1.7e-227) {
		tmp = (180.0 * atan(((A * -2.0) / B))) / ((double) M_PI);
	} else if (B <= 3.3e-21) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} 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 <= -2.1e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.9e-217) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 1.7e-227) {
		tmp = (180.0 * Math.atan(((A * -2.0) / B))) / Math.PI;
	} else if (B <= 3.3e-21) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.1e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.9e-217:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 1.7e-227:
		tmp = (180.0 * math.atan(((A * -2.0) / B))) / math.pi
	elif B <= 3.3e-21:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.1e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.9e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 1.7e-227)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(A * -2.0) / B))) / pi);
	elseif (B <= 3.3e-21)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	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 <= -2.1e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.9e-217)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 1.7e-227)
		tmp = (180.0 * atan(((A * -2.0) / B))) / pi;
	elseif (B <= 3.3e-21)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.1e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.9e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-227], N[(N[(180.0 * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.3e-21], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.1e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -2.1e-18 < B < -1.89999999999999993e-217

   1. Initial program 34.7%

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

   4. Applied egg-rr 57.7%

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

   5. Taylor expanded in C around inf 47.9%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 47.9%

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

      9. distribute-lft-neg-in 47.9%

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

      10. metadata-eval 47.9%

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

      11. associate-*r/ 47.9%

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

      12. *-commutative 47.9%

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

      13. associate-/l* 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in B around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. *-commutative 47.8%

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

      4. associate-*r/ 47.8%

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

      5. associate-*l/ 47.9%

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

   10. Simplified 47.9%

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

   if -1.89999999999999993e-217 < B < 1.69999999999999989e-227

   1. Initial program 70.9%

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

      1. associate-*r/ 70.9%

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

      2. associate-*l/ 70.9%

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

      3. *-un-lft-identity 70.9%

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

      4. unpow2 70.9%

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

      5. unpow2 70.9%

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

      6. hypot-define 81.7%

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

   4. Applied egg-rr 81.7%

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

   5. Taylor expanded in A around inf 57.0%

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

      1. *-commutative 57.0%

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

   7. Simplified 57.0%

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

   if 1.69999999999999989e-227 < B < 3.30000000000000009e-21

   1. Initial program 51.5%

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

   4. Applied egg-rr 71.0%

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

   5. Taylor expanded in A around -inf 46.6%

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

   if 3.30000000000000009e-21 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

Alternative 18: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -8.3e-215)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (<= B 9.6e-228)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B 2.25e-21)
         (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.3e-215) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 9.6e-228) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.25e-21) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.3e-215) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 9.6e-228) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.25e-21) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.3e-215:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 9.6e-228:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.25e-21:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.3e-215)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 9.6e-228)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.25e-21)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.3e-215)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 9.6e-228)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.25e-21)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.3e-215], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.6e-228], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.25e-21], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.1999999999999999e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -3.1999999999999999e-18 < B < -8.3000000000000004e-215

   1. Initial program 34.7%

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

   4. Applied egg-rr 57.7%

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

   5. Taylor expanded in C around inf 47.9%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 47.9%

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

      9. distribute-lft-neg-in 47.9%

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

      10. metadata-eval 47.9%

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

      11. associate-*r/ 47.9%

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

      12. *-commutative 47.9%

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

      13. associate-/l* 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in B around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. *-commutative 47.8%

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

      4. associate-*r/ 47.8%

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

      5. associate-*l/ 47.9%

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

   10. Simplified 47.9%

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

   if -8.3000000000000004e-215 < B < 9.60000000000000008e-228

   1. Initial program 70.9%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 9.60000000000000008e-228 < B < 2.24999999999999984e-21

   1. Initial program 51.5%

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

   4. Applied egg-rr 71.0%

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

   5. Taylor expanded in A around -inf 46.6%

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

   if 2.24999999999999984e-21 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 9.6 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.95 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.9e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -2.95e-217)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (<= B 1.75e-227)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B 1.65e-20)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.95e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 1.75e-227) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 1.65e-20) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} 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 <= -2.9e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.95e-217) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 1.75e-227) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 1.65e-20) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.9e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.95e-217:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 1.75e-227:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 1.65e-20:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.9e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.95e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 1.75e-227)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 1.65e-20)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	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 <= -2.9e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.95e-217)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 1.75e-227)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 1.65e-20)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.9e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.95e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.75e-227], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.65e-20], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.9e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -2.9e-18 < B < -2.9499999999999999e-217

   1. Initial program 34.7%

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

   4. Applied egg-rr 57.7%

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

   5. Taylor expanded in C around inf 47.9%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 47.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 47.9%

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

      9. distribute-lft-neg-in 47.9%

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

      10. metadata-eval 47.9%

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

      11. associate-*r/ 47.9%

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

      12. *-commutative 47.9%

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

      13. associate-/l* 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in B around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. *-commutative 47.8%

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

      4. associate-*r/ 47.8%

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

      5. associate-*l/ 47.9%

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

   10. Simplified 47.9%

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

   if -2.9499999999999999e-217 < B < 1.75000000000000005e-227

   1. Initial program 70.9%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 1.75000000000000005e-227 < B < 1.65e-20

   1. Initial program 51.5%

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

   3. Taylor expanded in A around -inf 46.6%

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

      1. associate-*r/ 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in B around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-/l* 46.6%

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

   8. Simplified 46.6%

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

   if 1.65e-20 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.95 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.2e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -6.8e-217)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (if (<= B 1.1e-227)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B 2.7e-21)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.2e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6.8e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 1.1e-227) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.7e-21) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} 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 <= -9.2e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6.8e-217) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 1.1e-227) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.7e-21) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.2e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6.8e-217:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 1.1e-227:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.7e-21:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.2e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6.8e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 1.1e-227)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.7e-21)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	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 <= -9.2e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6.8e-217)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 1.1e-227)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.7e-21)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.2e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.8e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-227], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-21], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -9.2000000000000004e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -9.2000000000000004e-18 < B < -6.80000000000000032e-217

   1. Initial program 34.7%

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

   3. Taylor expanded in C around inf 47.8%

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

   4. Taylor expanded in A around inf 47.8%

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

   6. Simplified 47.9%

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

   if -6.80000000000000032e-217 < B < 1.0999999999999999e-227

   1. Initial program 70.9%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 1.0999999999999999e-227 < B < 2.7000000000000001e-21

   1. Initial program 51.5%

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

   3. Taylor expanded in A around -inf 46.6%

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

      1. associate-*r/ 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in B around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-/l* 46.6%

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

   8. Simplified 46.6%

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

   if 2.7000000000000001e-21 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.9e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -6e-215)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (if (<= B 4.9e-228)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B 1.9e-20)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6e-215) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= 4.9e-228) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 1.9e-20) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} 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 <= -2.9e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6e-215) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= 4.9e-228) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 1.9e-20) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.9e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6e-215:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= 4.9e-228:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 1.9e-20:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.9e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6e-215)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= 4.9e-228)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 1.9e-20)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	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 <= -2.9e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6e-215)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= 4.9e-228)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 1.9e-20)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.9e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6e-215], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.9e-228], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-20], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.9e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -2.9e-18 < B < -6.00000000000000051e-215

   1. Initial program 34.7%

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

   3. Taylor expanded in C around inf 47.8%

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

   4. Taylor expanded in A around inf 47.8%

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

   if -6.00000000000000051e-215 < B < 4.89999999999999988e-228

   1. Initial program 70.9%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 4.89999999999999988e-228 < B < 1.8999999999999999e-20

   1. Initial program 51.5%

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

   3. Taylor expanded in A around -inf 46.6%

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

      1. associate-*r/ 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in B around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-/l* 46.6%

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

   8. Simplified 46.6%

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

   if 1.8999999999999999e-20 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.62 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.6e-18)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -7.6e-217)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (if (<= B 6.2e-228)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B 1.62e-21)
         (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-18) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.6e-217) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= 6.2e-228) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 1.62e-21) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-18) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.6e-217) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= 6.2e-228) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 1.62e-21) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.6e-18:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.6e-217:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= 6.2e-228:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 1.62e-21:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.6e-18)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.6e-217)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= 6.2e-228)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 1.62e-21)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.6e-18)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.6e-217)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= 6.2e-228)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 1.62e-21)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.6e-18], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.6e-217], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.2e-228], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.62e-21], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $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 < -3.6000000000000001e-18

   1. Initial program 41.9%

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

   3. Taylor expanded in B around -inf 68.2%

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

   if -3.6000000000000001e-18 < B < -7.59999999999999974e-217

   1. Initial program 34.7%

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

   3. Taylor expanded in C around inf 47.8%

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

   4. Taylor expanded in A around inf 47.8%

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

   if -7.59999999999999974e-217 < B < 6.1999999999999996e-228

   1. Initial program 70.9%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 6.1999999999999996e-228 < B < 1.62000000000000003e-21

   1. Initial program 51.5%

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

   3. Taylor expanded in A around -inf 46.6%

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

      1. associate-*r/ 46.6%

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

   5. Simplified 46.6%

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

      1. add-cube-cbrt 46.2%

         \[\leadsto 180 \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}} \cdot \sqrt[3]{\frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}}\right) \cdot \sqrt[3]{\frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}}\right)} \]

      2. pow3 46.2%

         \[\leadsto 180 \cdot \color{blue}{{\left(\sqrt[3]{\frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}}\right)}^{3}} \]

      3. associate-/l* 46.2%

         \[\leadsto 180 \cdot {\left(\sqrt[3]{\frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi}}\right)}^{3} \]

   7. Applied egg-rr 46.2%

      \[\leadsto 180 \cdot \color{blue}{{\left(\sqrt[3]{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}}\right)}^{3}} \]

   8. Taylor expanded in B around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-/l* 46.6%

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

   10. Simplified 46.6%

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

   if 1.62000000000000003e-21 < B

   1. Initial program 55.1%

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

   3. Taylor expanded in B around inf 60.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.6 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.62 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 58.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -2.35 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A + B}{-B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))))
   (if (<= B -8.5e-32)
     t_0
     (if (<= B -2.35e-213)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (if (<= B 2.4e-16) t_0 (/ 180.0 (/ PI (atan (/ (+ A B) (- B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -8.5e-32) {
		tmp = t_0;
	} else if (B <= -2.35e-213) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else if (B <= 2.4e-16) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((A + B) / -B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	double tmp;
	if (B <= -8.5e-32) {
		tmp = t_0;
	} else if (B <= -2.35e-213) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else if (B <= 2.4e-16) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((A + B) / -B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	tmp = 0
	if B <= -8.5e-32:
		tmp = t_0
	elif B <= -2.35e-213:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	elif B <= 2.4e-16:
		tmp = t_0
	else:
		tmp = 180.0 / (math.pi / math.atan(((A + B) / -B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi))
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = t_0;
	elseif (B <= -2.35e-213)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	elseif (B <= 2.4e-16)
		tmp = t_0;
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(A + B) / Float64(-B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = t_0;
	elseif (B <= -2.35e-213)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	elseif (B <= 2.4e-16)
		tmp = t_0;
	else
		tmp = 180.0 / (pi / atan(((A + B) / -B)));
	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[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8.5e-32], t$95$0, If[LessEqual[B, -2.35e-213], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-16], t$95$0, N[(180.0 / N[(Pi / N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.5000000000000003e-32 or -2.35e-213 < B < 2.40000000000000005e-16

   1. Initial program 52.4%

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

   3. Taylor expanded in B around -inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. div-sub 68.7%

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

   5. Simplified 68.7%

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

   if -8.5000000000000003e-32 < B < -2.35e-213

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if 2.40000000000000005e-16 < B

   1. Initial program 53.7%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in C around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-neg-frac2 49.9%

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

      3. unpow2 49.9%

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

      4. unpow2 49.9%

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

      5. hypot-define 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in A around 0 69.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.35 \cdot 10^{-213}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A + B}{-B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 45.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.5e-32)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.15e-230)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (if (<= B 5.8e-20)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.15e-230) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else if (B <= 5.8e-20) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((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 <= -8.5e-32) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.15e-230) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else if (B <= 5.8e-20) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.5e-32:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.15e-230:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	elif B <= 5.8e-20:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / 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 <= -8.5e-32)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.15e-230)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	elseif (B <= 5.8e-20)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / 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 <= -8.5e-32)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.15e-230)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	elseif (B <= 5.8e-20)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.5e-32], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.15e-230], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.8e-20], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

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

   3. Taylor expanded in B around -inf 66.9%

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

   if -8.5000000000000003e-32 < B < -1.1499999999999999e-230

   1. Initial program 34.7%

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

      1. associate-*r/ 34.7%

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

      2. associate-*l/ 34.7%

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

      3. *-un-lft-identity 34.7%

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

      4. unpow2 34.7%

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

      5. unpow2 34.7%

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

      6. hypot-define 57.7%

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

   4. Applied egg-rr 57.7%

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

   5. Taylor expanded in C around inf 32.8%

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

      1. distribute-rgt1-in 32.8%

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

      2. metadata-eval 32.8%

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

      3. mul0-lft 32.8%

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

      4. metadata-eval 32.8%

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

   7. Simplified 32.8%

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

   if -1.1499999999999999e-230 < B < 5.8e-20

   1. Initial program 59.9%

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

   3. Taylor expanded in A around inf 41.0%

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

   if 5.8e-20 < B

   1. Initial program 54.4%

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

   3. Taylor expanded in B around inf 61.5%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 62.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.45 \cdot 10^{-216}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - t\_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)))
   (if (<= B -8.5e-32)
     (* 180.0 (/ (atan (- 1.0 t_0)) PI))
     (if (<= B -2.45e-216)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
       (* 180.0 (/ (atan (- -1.0 t_0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (atan((1.0 - t_0)) / ((double) M_PI));
	} else if (B <= -2.45e-216) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else {
		tmp = 180.0 * (atan((-1.0 - t_0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (Math.atan((1.0 - t_0)) / Math.PI);
	} else if (B <= -2.45e-216) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - t_0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	tmp = 0
	if B <= -8.5e-32:
		tmp = 180.0 * (math.atan((1.0 - t_0)) / math.pi)
	elif B <= -2.45e-216:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	else:
		tmp = 180.0 * (math.atan((-1.0 - t_0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - t_0)) / pi));
	elseif (B <= -2.45e-216)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - t_0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = 180.0 * (atan((1.0 - t_0)) / pi);
	elseif (B <= -2.45e-216)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	else
		tmp = 180.0 * (atan((-1.0 - t_0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -8.5e-32], N[(180.0 * N[(N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.45e-216], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

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

   3. Taylor expanded in B around -inf 81.4%

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

      1. associate--l+ 81.4%

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

      2. div-sub 81.4%

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

   5. Simplified 81.4%

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

   if -8.5000000000000003e-32 < B < -2.4500000000000001e-216

   1. Initial program 30.7%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in C around inf 44.8%

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

      1. distribute-rgt1-in 44.8%

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

      2. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      3. mul0-lft 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B} + -0.5 \cdot \frac{B}{C}\right)}} \]

      4. div0 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      5. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{0} + -0.5 \cdot \frac{B}{C}\right)}} \]

      6. metadata-eval 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(0 + \color{blue}{\left(-0.5\right)} \cdot \frac{B}{C}\right)}} \]

      7. cancel-sign-sub-inv 44.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0 - 0.5 \cdot \frac{B}{C}\right)}}} \]

      8. neg-sub0 44.8%

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

      9. distribute-lft-neg-in 44.8%

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

      10. metadata-eval 44.8%

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

      11. associate-*r/ 44.8%

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

      12. *-commutative 44.8%

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

      13. associate-/l* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in B around 0 44.6%

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

      1. associate-*r/ 44.7%

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

      2. associate-*r/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*r/ 44.6%

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

      5. associate-*l/ 44.8%

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

   10. Simplified 44.8%

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

   if -2.4500000000000001e-216 < B

   1. Initial program 58.0%

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

      1. +-commutative 58.0%

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

      2. unpow2 58.0%

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

      3. unpow2 58.0%

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

      4. hypot-undefine 77.9%

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

      5. sub-neg 77.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\pi} \]

      6. distribute-lft-in 68.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\pi} \]

      7. hypot-undefine 55.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      8. unpow2 55.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)}{\pi} \]

      9. unpow2 55.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      10. +-commutative 55.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      11. unpow2 55.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)\right)}{\pi} \]

      12. unpow2 55.7%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      13. hypot-define 68.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)\right)}{\pi} \]

   4. Applied egg-rr 68.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(A - C, B\right)\right)\right)}}{\pi} \]

   5. Taylor expanded in B around inf 66.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \color{blue}{\left(\frac{A}{B} + 1\right)}\right)}{\pi} \]

      2. associate--r+ 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)}}{\pi} \]

      3. div-sub 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{\frac{C - A}{B}} - 1\right)}{\pi} \]

      4. sub-neg 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - A}{B} + \left(-1\right)\right)}}{\pi} \]

      5. metadata-eval 66.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + \color{blue}{-1}\right)}{\pi} \]

   7. Simplified 66.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - A}{B} + -1\right)}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.45 \cdot 10^{-216}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A - C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 44.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-113}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.5e-32)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.7e-113)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.7e-113) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.7e-113) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.5e-32:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.7e-113:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.7e-113)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.7e-113)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.5e-32], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-113], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.5000000000000003e-32

   1. Initial program 43.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 66.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -8.5000000000000003e-32 < B < 1.7000000000000001e-113

   1. Initial program 49.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 49.4%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]

      2. associate-*l/ 49.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      3. *-un-lft-identity 49.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 49.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 49.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}{B}\right)}{\pi} \]

      6. hypot-define 70.3%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A - C, B\right)}}{B}\right)}{\pi} \]

   4. Applied egg-rr 70.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}} \]

   5. Taylor expanded in C around inf 27.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. distribute-rgt1-in 27.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      2. metadata-eval 27.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      3. mul0-lft 27.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      4. metadata-eval 27.7%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   7. Simplified 27.7%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   if 1.7000000000000001e-113 < B

   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 B around inf 49.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 44.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.5e-32)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e-113)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-113) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-113) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.5e-32:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-113:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.5e-32)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-113)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.5e-32)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-113)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.5e-32], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-113], 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 < -8.5000000000000003e-32

   1. Initial program 43.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 66.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -8.5000000000000003e-32 < B < 4.80000000000000024e-113

   1. Initial program 49.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 27.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}}{\pi} \]

      2. distribute-rgt1-in 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      3. metadata-eval 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 27.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 4.80000000000000024e-113 < B

   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 B around inf 49.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 28: 44.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.5e-32)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.9e-113)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.5e-32) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.9e-113) {
		tmp = 180.0 * (atan(0.0) / ((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 <= -8.5e-32) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.9e-113) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.5e-32:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.9e-113:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -8.5e-32)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.9e-113)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -8.5e-32)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.9e-113)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.5e-32], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.9e-113], N[(180.0 * N[(N[ArcTan[0.0], $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 < -8.5000000000000003e-32

   1. Initial program 43.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 66.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -8.5000000000000003e-32 < B < 3.8999999999999999e-113

   1. Initial program 49.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 49.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      2. unpow2 49.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)\right)}{\pi} \]

      3. unpow2 49.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      4. hypot-undefine 70.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right)}{\pi} \]

      5. sub-neg 70.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\pi} \]

      6. distribute-lft-in 45.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\pi} \]

      7. hypot-undefine 43.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      8. unpow2 43.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)}{\pi} \]

      9. unpow2 43.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      10. +-commutative 43.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      11. unpow2 43.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)\right)}{\pi} \]

      12. unpow2 43.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      13. hypot-define 45.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)\right)}{\pi} \]

   4. Applied egg-rr 45.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(A - C, B\right)\right)\right)}}{\pi} \]

   5. Taylor expanded in A around -inf 14.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. distribute-lft1-in 14.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)}}{\pi} \]

      2. metadata-eval 14.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} \cdot \frac{C}{B}\right)}{\pi} \]

      3. mul0-lft 27.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   7. Simplified 27.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 3.8999999999999999e-113 < B

   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 B around inf 49.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 29: 29.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.3 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.3e-113) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.3e-113) {
		tmp = 180.0 * (atan(0.0) / ((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 <= 1.3e-113) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.3e-113:
		tmp = 180.0 * (math.atan(0.0) / 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 <= 1.3e-113)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= 1.3e-113)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.3e-113], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.3e-113

   1. Initial program 46.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 46.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      2. unpow2 46.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)\right)}{\pi} \]

      3. unpow2 46.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      4. hypot-undefine 77.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right)}{\pi} \]

      5. sub-neg 77.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\pi} \]

      6. distribute-lft-in 64.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\pi} \]

      7. hypot-undefine 43.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      8. unpow2 43.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)}{\pi} \]

      9. unpow2 43.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      10. +-commutative 43.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      11. unpow2 43.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)\right)}{\pi} \]

      12. unpow2 43.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      13. hypot-define 64.0%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)\right)}{\pi} \]

   4. Applied egg-rr 64.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(A - C, B\right)\right)\right)}}{\pi} \]

   5. Taylor expanded in A around -inf 9.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. distribute-lft1-in 9.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)}}{\pi} \]

      2. metadata-eval 9.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} \cdot \frac{C}{B}\right)}{\pi} \]

      3. mul0-lft 16.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   7. Simplified 16.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 1.3e-113 < B

   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 B around inf 49.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 21.3% 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 50.0%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Add Preprocessing

3. Taylor expanded in B around inf 20.0%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024103 
(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)))