ABCF->ab-angle angle

Percentage Accurate: 54.9% → 81.6%

Time: 26.9s

Alternatives: 18

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: 54.9% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.8e+122)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+122) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+122) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.8e+122:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.8e+122)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - 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 <= -4.8e+122)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.8e+122], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if A < -4.8000000000000004e122

   1. Initial program 13.3%

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

   3. Taylor expanded in A around -inf 77.1%

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

      1. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.9%

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

      3. associate-/l* 75.9%

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

   7. Applied egg-rr 75.9%

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

      1. associate-/r/ 77.3%

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

      2. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if -4.8000000000000004e122 < A

   1. Initial program 60.4%

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

   3. Simplified 86.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.05 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.05e+40)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 1.8e+178)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.05e+40) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 1.8e+178) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.05e+40) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 1.8e+178) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.05e+40:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 1.8e+178:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.05e+40)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 1.8e+178)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.05e+40)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 1.8e+178)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.05e+40], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.8e+178], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.0500000000000001e40

   1. Initial program 79.4%

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

   3. Taylor expanded in A around 0 79.4%

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

      1. unpow2 79.4%

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

      2. unpow2 79.4%

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

      3. hypot-define 96.7%

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

   5. Simplified 96.7%

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

   if -2.0500000000000001e40 < C < 1.7999999999999999e178

   1. Initial program 48.1%

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

   3. Taylor expanded in C around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. distribute-neg-frac2 47.0%

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

      3. +-commutative 47.0%

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

      4. unpow2 47.0%

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

      5. unpow2 47.0%

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

      6. hypot-define 77.0%

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

   5. Simplified 77.0%

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

   if 1.7999999999999999e178 < C

   1. Initial program 8.9%

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

   3. Taylor expanded in A around 0 8.9%

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

      1. unpow2 8.9%

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

      2. unpow2 8.9%

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

      3. hypot-define 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in C around inf 88.9%

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

      1. associate-*r/ 88.9%

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

   8. Simplified 88.9%

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

   9. Taylor expanded in B around 0 88.9%

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

       1. associate-*r/ 89.0%

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

       2. *-commutative 89.0%

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

       3. associate-/l* 89.0%

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

   11. Simplified 89.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.05 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e+128)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (if (<= A 1.1e+57)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+128) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else if (A <= 1.1e+57) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+128) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else if (A <= 1.1e+57) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e+128:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	elif A <= 1.1e+57:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e+128)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	elseif (A <= 1.1e+57)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e+128)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	elseif (A <= 1.1e+57)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e+128], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.1e+57], 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[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.50000000000000045e128

   1. Initial program 13.3%

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

   3. Taylor expanded in A around -inf 77.1%

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

      1. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.9%

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

      3. associate-/l* 75.9%

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

   7. Applied egg-rr 75.9%

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

      1. associate-/r/ 77.3%

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

      2. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if -8.50000000000000045e128 < A < 1.1e57

   1. Initial program 54.1%

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

   3. Taylor expanded in A around 0 51.2%

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

      1. unpow2 51.2%

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

      2. unpow2 51.2%

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

      3. hypot-define 79.8%

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

   5. Simplified 79.8%

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

   if 1.1e57 < A

   1. Initial program 78.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in B around inf 89.6%

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

      1. +-commutative 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.3e+124)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.3e+124) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.3e+124) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.3e+124:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.3e+124)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.3e+124)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.3e+124], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.30000000000000015e124

   1. Initial program 13.3%

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

   3. Taylor expanded in A around -inf 77.1%

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

      1. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.9%

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

      3. associate-/l* 75.9%

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

   7. Applied egg-rr 75.9%

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

      1. associate-/r/ 77.3%

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

      2. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if -3.30000000000000015e124 < A

   1. Initial program 60.4%

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

   3. Simplified 86.5%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-295}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 2.85 \cdot 10^{-123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI)))
        (t_1 (* 180.0 (/ (atan -1.0) PI)))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -3.6e-25)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 9e-295)
       t_0
       (if (<= B 6e-183)
         t_2
         (if (<= B 2.85e-123)
           t_0
           (if (<= B 2.35e-89)
             t_1
             (if (<= B 1.85e-76) t_2 (if (<= B 2.4e-30) t_0 t_1)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -3.6e-25) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9e-295) {
		tmp = t_0;
	} else if (B <= 6e-183) {
		tmp = t_2;
	} else if (B <= 2.85e-123) {
		tmp = t_0;
	} else if (B <= 2.35e-89) {
		tmp = t_1;
	} else if (B <= 1.85e-76) {
		tmp = t_2;
	} else if (B <= 2.4e-30) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -3.6e-25) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9e-295) {
		tmp = t_0;
	} else if (B <= 6e-183) {
		tmp = t_2;
	} else if (B <= 2.85e-123) {
		tmp = t_0;
	} else if (B <= 2.35e-89) {
		tmp = t_1;
	} else if (B <= 1.85e-76) {
		tmp = t_2;
	} else if (B <= 2.4e-30) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	t_1 = 180.0 * (math.atan(-1.0) / math.pi)
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -3.6e-25:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9e-295:
		tmp = t_0
	elif B <= 6e-183:
		tmp = t_2
	elif B <= 2.85e-123:
		tmp = t_0
	elif B <= 2.35e-89:
		tmp = t_1
	elif B <= 1.85e-76:
		tmp = t_2
	elif B <= 2.4e-30:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(-1.0) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -3.6e-25)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9e-295)
		tmp = t_0;
	elseif (B <= 6e-183)
		tmp = t_2;
	elseif (B <= 2.85e-123)
		tmp = t_0;
	elseif (B <= 2.35e-89)
		tmp = t_1;
	elseif (B <= 1.85e-76)
		tmp = t_2;
	elseif (B <= 2.4e-30)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	t_1 = 180.0 * (atan(-1.0) / pi);
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -3.6e-25)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9e-295)
		tmp = t_0;
	elseif (B <= 6e-183)
		tmp = t_2;
	elseif (B <= 2.85e-123)
		tmp = t_0;
	elseif (B <= 2.35e-89)
		tmp = t_1;
	elseif (B <= 1.85e-76)
		tmp = t_2;
	elseif (B <= 2.4e-30)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.6e-25], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-295], t$95$0, If[LessEqual[B, 6e-183], t$95$2, If[LessEqual[B, 2.85e-123], t$95$0, If[LessEqual[B, 2.35e-89], t$95$1, If[LessEqual[B, 1.85e-76], t$95$2, If[LessEqual[B, 2.4e-30], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.5999999999999999e-25

   1. Initial program 45.6%

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

   3. Taylor expanded in B around -inf 62.9%

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

   if -3.5999999999999999e-25 < B < 9.0000000000000003e-295 or 5.9999999999999996e-183 < B < 2.85000000000000014e-123 or 1.85000000000000006e-76 < B < 2.39999999999999985e-30

   1. Initial program 61.1%

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

   3. Taylor expanded in A around 0 48.5%

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

      1. unpow2 48.5%

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

      2. unpow2 48.5%

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

      3. hypot-define 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in B around -inf 44.0%

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

      1. +-commutative 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in C around inf 41.8%

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

   if 9.0000000000000003e-295 < B < 5.9999999999999996e-183 or 2.34999999999999998e-89 < B < 1.85000000000000006e-76

   1. Initial program 45.6%

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

   3. Taylor expanded in C around inf 54.1%

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

      1. associate-*r/ 54.1%

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

      2. distribute-rgt1-in 54.1%

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

      3. metadata-eval 54.1%

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

      4. mul0-lft 54.1%

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

      5. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   if 2.85000000000000014e-123 < B < 2.34999999999999998e-89 or 2.39999999999999985e-30 < B

   1. Initial program 48.3%

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

   3. Taylor expanded in B around inf 58.8%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.85 \cdot 10^{-123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-155}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ A (- B))) PI))))
   (if (<= B -1.2e-61)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 1.3e-285)
       (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
       (if (<= B 2.1e-181)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 3.6e-155)
           t_0
           (if (<= B 8e-85)
             (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
             (if (<= B 1.8e-74)
               t_0
               (if (<= B 4.2e-17)
                 (* 180.0 (/ (atan (/ C B)) PI))
                 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.2e-61) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.3e-285) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 2.1e-181) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.6e-155) {
		tmp = t_0;
	} else if (B <= 8e-85) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 1.8e-74) {
		tmp = t_0;
	} else if (B <= 4.2e-17) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((A / -B)) / Math.PI);
	double tmp;
	if (B <= -1.2e-61) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.3e-285) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 2.1e-181) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.6e-155) {
		tmp = t_0;
	} else if (B <= 8e-85) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 1.8e-74) {
		tmp = t_0;
	} else if (B <= 4.2e-17) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((A / -B)) / math.pi)
	tmp = 0
	if B <= -1.2e-61:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.3e-285:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 2.1e-181:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.6e-155:
		tmp = t_0
	elif B <= 8e-85:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 1.8e-74:
		tmp = t_0
	elif B <= 4.2e-17:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi))
	tmp = 0.0
	if (B <= -1.2e-61)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.3e-285)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 2.1e-181)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.6e-155)
		tmp = t_0;
	elseif (B <= 8e-85)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 1.8e-74)
		tmp = t_0;
	elseif (B <= 4.2e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((A / -B)) / pi);
	tmp = 0.0;
	if (B <= -1.2e-61)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.3e-285)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 2.1e-181)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.6e-155)
		tmp = t_0;
	elseif (B <= 8e-85)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 1.8e-74)
		tmp = t_0;
	elseif (B <= 4.2e-17)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.2e-61], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-285], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-181], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-155], t$95$0, If[LessEqual[B, 8e-85], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-74], t$95$0, If[LessEqual[B, 4.2e-17], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -1.2e-61

   1. Initial program 45.3%

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

   3. Taylor expanded in B around -inf 59.3%

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

   if -1.2e-61 < B < 1.3000000000000001e-285

   1. Initial program 68.6%

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

   3. Taylor expanded in A around inf 52.9%

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

   if 1.3000000000000001e-285 < B < 2.10000000000000003e-181

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

      1. associate-*r/ 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. metadata-eval 54.6%

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

   5. Simplified 54.6%

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

   if 2.10000000000000003e-181 < B < 3.59999999999999989e-155 or 7.9999999999999998e-85 < B < 1.8000000000000001e-74

   1. Initial program 85.1%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in B around -inf 75.5%

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

      1. neg-mul-1 75.5%

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

      2. unsub-neg 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in A around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-neg-frac2 75.5%

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

   10. Simplified 75.5%

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

   if 3.59999999999999989e-155 < B < 7.9999999999999998e-85

   1. Initial program 39.6%

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

   3. Taylor expanded in A around 0 39.9%

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

      1. unpow2 39.9%

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

      2. unpow2 39.9%

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

      3. hypot-define 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in C around inf 34.7%

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

      1. associate-*r/ 34.7%

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

   8. Simplified 34.7%

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

   if 1.8000000000000001e-74 < B < 4.19999999999999984e-17

   1. Initial program 48.2%

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

   3. Taylor expanded in A around 0 49.2%

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

      1. unpow2 49.2%

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

      2. unpow2 49.2%

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

      3. hypot-define 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in B around -inf 40.0%

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

      1. +-commutative 40.0%

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

   8. Simplified 40.0%

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

   9. Taylor expanded in C around inf 40.1%

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

   if 4.19999999999999984e-17 < B

   1. Initial program 46.4%

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

   3. Taylor expanded in B around inf 62.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-285}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.55 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3e-63)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.5e-295)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= B 7.5e-182)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 3.55e-152)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (if (<= B 1.85e-22)
           (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.5e-295) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 7.5e-182) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.55e-152) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 1.85e-22) {
		tmp = 180.0 * (atan(((0.5 * B) / 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 <= -3e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.5e-295) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 7.5e-182) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.55e-152) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 1.85e-22) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / 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 <= -3e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.5e-295:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 7.5e-182:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.55e-152:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 1.85e-22:
		tmp = 180.0 * (math.atan(((0.5 * B) / 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 <= -3e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.5e-295)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 7.5e-182)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.55e-152)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 1.85e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / 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 <= -3e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.5e-295)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 7.5e-182)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.55e-152)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 1.85e-22)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-295], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.5e-182], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.55e-152], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-22], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -2.99999999999999979e-63

   1. Initial program 45.3%

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

   3. Taylor expanded in B around -inf 59.3%

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

   if -2.99999999999999979e-63 < B < 9.5e-295

   1. Initial program 68.6%

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

   3. Taylor expanded in A around inf 52.9%

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

   if 9.5e-295 < B < 7.49999999999999935e-182

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

      1. associate-*r/ 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. metadata-eval 54.6%

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

   5. Simplified 54.6%

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

   if 7.49999999999999935e-182 < B < 3.55000000000000005e-152

   1. Initial program 82.3%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in B around -inf 70.5%

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

      1. neg-mul-1 70.5%

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

      2. unsub-neg 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in A around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-neg-frac2 70.8%

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

   10. Simplified 70.8%

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

   if 3.55000000000000005e-152 < B < 1.85e-22

   1. Initial program 43.0%

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

   3. Taylor expanded in A around -inf 54.6%

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

      1. associate-*r/ 54.6%

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

   5. Simplified 54.6%

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

   if 1.85e-22 < B

   1. Initial program 47.8%

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

   3. Taylor expanded in B around inf 61.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.55 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-115}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ A (- B))) PI))))
   (if (<= B -4.1e-63)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 4.8e-295)
       t_0
       (if (<= B 6e-181)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 2.7e-115) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double tmp;
	if (B <= -4.1e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-295) {
		tmp = t_0;
	} else if (B <= 6e-181) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.7e-115) {
		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((A / -B)) / Math.PI);
	double tmp;
	if (B <= -4.1e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-295) {
		tmp = t_0;
	} else if (B <= 6e-181) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.7e-115) {
		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((A / -B)) / math.pi)
	tmp = 0
	if B <= -4.1e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-295:
		tmp = t_0
	elif B <= 6e-181:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.7e-115:
		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(A / Float64(-B))) / pi))
	tmp = 0.0
	if (B <= -4.1e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-295)
		tmp = t_0;
	elseif (B <= 6e-181)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.7e-115)
		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((A / -B)) / pi);
	tmp = 0.0;
	if (B <= -4.1e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-295)
		tmp = t_0;
	elseif (B <= 6e-181)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.7e-115)
		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[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.1e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-295], t$95$0, If[LessEqual[B, 6e-181], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-115], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.0999999999999998e-63

   1. Initial program 45.3%

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

   3. Taylor expanded in B around -inf 59.3%

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

   if -4.0999999999999998e-63 < B < 4.7999999999999996e-295 or 5.99999999999999948e-181 < B < 2.7e-115

   1. Initial program 67.1%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in B around -inf 64.5%

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

      1. neg-mul-1 64.5%

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

      2. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in A around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-neg-frac2 52.5%

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

   10. Simplified 52.5%

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

   if 4.7999999999999996e-295 < B < 5.99999999999999948e-181

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

      1. associate-*r/ 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. metadata-eval 54.6%

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

   5. Simplified 54.6%

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

   if 2.7e-115 < B

   1. Initial program 46.9%

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

   3. Taylor expanded in B around inf 51.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-58)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9e-294)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= B 3.9e-182)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 2.3e-114)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-58) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9e-294) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 3.9e-182) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.3e-114) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-58) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9e-294) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 3.9e-182) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.3e-114) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.2e-58:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9e-294:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 3.9e-182:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.3e-114:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.2e-58)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 3.9e-182)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.3e-114)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.2e-58)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9e-294)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 3.9e-182)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.3e-114)
		tmp = 180.0 * (atan((A / -B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.2e-58], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-294], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.9e-182], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.3e-114], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $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 < -7.20000000000000019e-58

   1. Initial program 45.3%

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

   3. Taylor expanded in B around -inf 59.3%

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

   if -7.20000000000000019e-58 < B < 8.99999999999999963e-294

   1. Initial program 68.6%

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

   3. Taylor expanded in A around inf 52.9%

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

   if 8.99999999999999963e-294 < B < 3.9e-182

   1. Initial program 44.3%

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

   3. Taylor expanded in C around inf 54.6%

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

      1. associate-*r/ 54.6%

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

      2. distribute-rgt1-in 54.6%

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

      3. metadata-eval 54.6%

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

      4. mul0-lft 54.6%

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

      5. metadata-eval 54.6%

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

   5. Simplified 54.6%

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

   if 3.9e-182 < B < 2.2999999999999999e-114

   1. Initial program 63.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in B around -inf 56.6%

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

      1. neg-mul-1 56.6%

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

      2. unsub-neg 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in A around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-neg-frac2 51.3%

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

   10. Simplified 51.3%

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

   if 2.2999999999999999e-114 < B

   1. Initial program 46.9%

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

   3. Taylor expanded in B around inf 51.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-190} \lor \neg \left(A \leq 2.8 \cdot 10^{+54}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e+32)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (if (or (<= A 2.4e-190) (not (<= A 2.8e+54)))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))
     (* 180.0 (/ (atan (/ (+ B C) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+32) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else if ((A <= 2.4e-190) || !(A <= 2.8e+54)) {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+32) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else if ((A <= 2.4e-190) || !(A <= 2.8e+54)) {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e+32:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	elif (A <= 2.4e-190) or not (A <= 2.8e+54):
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e+32)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	elseif ((A <= 2.4e-190) || !(A <= 2.8e+54))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e+32)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	elseif ((A <= 2.4e-190) || ~((A <= 2.8e+54)))
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e+32], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 2.4e-190], N[Not[LessEqual[A, 2.8e+54]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.1000000000000001e32

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.2%

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

      1. associate-*r/ 69.2%

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

   5. Simplified 69.2%

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

      1. clear-num 68.7%

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

      2. un-div-inv 68.7%

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

      3. associate-/l* 68.7%

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

   7. Applied egg-rr 68.7%

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

      1. associate-/r/ 69.4%

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

      2. associate-*r/ 69.4%

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

   9. Simplified 69.4%

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

   if -2.1000000000000001e32 < A < 2.4e-190 or 2.80000000000000015e54 < A

   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. Step-by-step derivation

   3. Simplified 88.4%

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

   5. Taylor expanded in B around inf 68.3%

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

      1. +-commutative 68.3%

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

   7. Simplified 68.3%

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

   if 2.4e-190 < A < 2.80000000000000015e54

   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 A around 0 46.3%

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

      1. unpow2 46.3%

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

      2. unpow2 46.3%

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

      3. hypot-define 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in B around -inf 61.5%

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

      1. +-commutative 61.5%

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

   8. Simplified 61.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-190} \lor \neg \left(A \leq 2.8 \cdot 10^{+54}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-190} \lor \neg \left(A \leq 7 \cdot 10^{+55}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.9e+31)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (if (or (<= A 1.5e-190) (not (<= A 7e+55)))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.9e+31) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else if ((A <= 1.5e-190) || !(A <= 7e+55)) {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.9e+31) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else if ((A <= 1.5e-190) || !(A <= 7e+55)) {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.9e+31:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	elif (A <= 1.5e-190) or not (A <= 7e+55):
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.9e+31)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	elseif ((A <= 1.5e-190) || !(A <= 7e+55))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.9e+31)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	elseif ((A <= 1.5e-190) || ~((A <= 7e+55)))
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.9e+31], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 1.5e-190], N[Not[LessEqual[A, 7e+55]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.8999999999999999e31

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.2%

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

      1. associate-*r/ 69.2%

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

   5. Simplified 69.2%

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

      1. clear-num 68.7%

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

      2. un-div-inv 68.7%

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

      3. associate-/l* 68.7%

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

   7. Applied egg-rr 68.7%

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

      1. associate-/r/ 69.4%

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

      2. associate-*r/ 69.4%

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

   9. Simplified 69.4%

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

   if -6.8999999999999999e31 < A < 1.4999999999999999e-190 or 7.00000000000000021e55 < A

   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. Step-by-step derivation

   3. Simplified 88.4%

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

   5. Taylor expanded in B around inf 68.3%

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

      1. +-commutative 68.3%

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

   7. Simplified 68.3%

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

   if 1.4999999999999999e-190 < A < 7.00000000000000021e55

   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. Step-by-step derivation

   3. Simplified 87.6%

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

   5. Taylor expanded in B around -inf 67.1%

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

      1. neg-mul-1 67.1%

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

      2. unsub-neg 67.1%

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

   7. Simplified 67.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-190} \lor \neg \left(A \leq 7 \cdot 10^{+55}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.06e+35)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (if (<= A 1.65e+74)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (/ (+ A B) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.06e+35) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else if (A <= 1.65e+74) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + B) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.06e+35) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else if (A <= 1.65e+74) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + B) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.06e+35:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	elif A <= 1.65e+74:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + B) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.06e+35)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	elseif (A <= 1.65e+74)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + B) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.06e+35)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	elseif (A <= 1.65e+74)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + B) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.06e+35], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.65e+74], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.0600000000000001e35

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.9%

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

      1. associate-*r/ 69.9%

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

   5. Simplified 69.9%

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

      1. clear-num 69.4%

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

      2. un-div-inv 69.4%

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

      3. associate-/l* 69.4%

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

   7. Applied egg-rr 69.4%

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

      1. associate-/r/ 70.1%

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

      2. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

   if -1.0600000000000001e35 < A < 1.6500000000000001e74

   1. Initial program 55.9%

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

   3. Taylor expanded in A around 0 53.5%

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

      1. unpow2 53.5%

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

      2. unpow2 53.5%

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

      3. hypot-define 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in B around -inf 52.4%

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

      1. +-commutative 52.4%

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

   8. Simplified 52.4%

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

   if 1.6500000000000001e74 < A

   1. Initial program 77.4%

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

   3. Taylor expanded in C around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-neg-frac2 77.4%

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

      3. +-commutative 77.4%

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

      4. unpow2 77.4%

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

      5. unpow2 77.4%

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

      6. hypot-define 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in A around 0 85.8%

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

      1. +-commutative 85.8%

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

   8. Simplified 85.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.25e+38)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 1.6e+74)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.25e+38) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.6e+74) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.25e+38) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.6e+74) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.25e+38:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.6e+74:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.25e+38)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.6e+74)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.25e+38)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.6e+74)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.25e+38], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.6e+74], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.25e38

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.9%

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

      1. associate-*r/ 69.9%

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

   5. Simplified 69.9%

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

   if -3.25e38 < A < 1.59999999999999997e74

   1. Initial program 55.9%

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

   3. Taylor expanded in A around 0 53.5%

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

      1. unpow2 53.5%

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

      2. unpow2 53.5%

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

      3. hypot-define 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in B around -inf 52.4%

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

      1. +-commutative 52.4%

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

   8. Simplified 52.4%

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

   if 1.59999999999999997e74 < A

   1. Initial program 77.4%

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

   3. Taylor expanded in A around inf 72.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e+42)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 2.45e+14)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (/ (- B A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+42) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 2.45e+14) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+42) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 2.45e+14) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e+42:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 2.45e+14:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e+42)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 2.45e+14)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e+42)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 2.45e+14)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e+42], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.45e+14], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.5500000000000001e42

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.9%

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

      1. associate-*r/ 69.9%

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

   5. Simplified 69.9%

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

   if -1.5500000000000001e42 < A < 2.45e14

   1. Initial program 55.6%

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

   3. Taylor expanded in A around 0 53.6%

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

      1. unpow2 53.6%

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

      2. unpow2 53.6%

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

      3. hypot-define 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in B around -inf 51.2%

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

      1. +-commutative 51.2%

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

   8. Simplified 51.2%

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

   if 2.45e14 < A

   1. Initial program 75.0%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in B around -inf 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in C around 0 73.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.45 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+33)
   (* (/ 180.0 PI) (atan (/ (* 0.5 B) A)))
   (if (<= A 2.6e+14)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (/ (- B A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+33) {
		tmp = (180.0 / ((double) M_PI)) * atan(((0.5 * B) / A));
	} else if (A <= 2.6e+14) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+33) {
		tmp = (180.0 / Math.PI) * Math.atan(((0.5 * B) / A));
	} else if (A <= 2.6e+14) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+33:
		tmp = (180.0 / math.pi) * math.atan(((0.5 * B) / A))
	elif A <= 2.6e+14:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+33)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(0.5 * B) / A)));
	elseif (A <= 2.6e+14)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+33)
		tmp = (180.0 / pi) * atan(((0.5 * B) / A));
	elseif (A <= 2.6e+14)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+33], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e+14], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.8000000000000001e33

   1. Initial program 22.3%

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

   3. Taylor expanded in A around -inf 69.9%

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

      1. associate-*r/ 69.9%

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

   5. Simplified 69.9%

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

      1. clear-num 69.4%

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

      2. un-div-inv 69.4%

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

      3. associate-/l* 69.4%

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

   7. Applied egg-rr 69.4%

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

      1. associate-/r/ 70.1%

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

      2. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

   if -1.8000000000000001e33 < A < 2.6e14

   1. Initial program 55.6%

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

   3. Taylor expanded in A around 0 53.6%

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

      1. unpow2 53.6%

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

      2. unpow2 53.6%

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

      3. hypot-define 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in B around -inf 51.2%

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

      1. +-commutative 51.2%

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

   8. Simplified 51.2%

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

   if 2.6e14 < A

   1. Initial program 75.0%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in B around -inf 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in C around 0 73.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.05e-157)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.5e-129)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-157) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.5e-129) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-157) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.5e-129) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.05e-157:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.5e-129:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.05e-157)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.5e-129)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.05e-157)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.5e-129)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.05e-157], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-129], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.05e-157

   1. Initial program 51.9%

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

   3. Taylor expanded in B around -inf 52.5%

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

   if -1.05e-157 < B < 6.49999999999999952e-129

   1. Initial program 56.4%

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

   3. Taylor expanded in C around inf 37.7%

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

      1. associate-*r/ 37.7%

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

      2. distribute-rgt1-in 37.7%

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

      3. metadata-eval 37.7%

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

      4. mul0-lft 37.7%

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

      5. metadata-eval 37.7%

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

   5. Simplified 37.7%

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

   if 6.49999999999999952e-129 < B

   1. Initial program 47.5%

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

   3. Taylor expanded in B around inf 50.9%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.4% accurate, 3.8× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 52.9%

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

   3. Taylor expanded in B around -inf 43.3%

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

   if -4.999999999999985e-310 < B

   1. Initial program 49.8%

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

   3. Taylor expanded in B around inf 41.0%

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

4. Final simplification 42.1%

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

Alternative 18: 21.5% 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 51.2%

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

3. Taylor expanded in B around inf 23.3%

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

4. Final simplification 23.3%

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

Reproduce

herbie shell --seed 2024044 
(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)))