ABCF->ab-angle angle

Percentage Accurate: 54.6% → 81.9%

Time: 23.1s

Alternatives: 19

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.6% 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: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+95)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (*
    180.0
    (log1p (expm1 (/ (atan (/ (- (- C A) (hypot (- A C) B)) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+95) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * log1p(expm1((atan((((C - A) - hypot((A - C), B)) / B)) / ((double) M_PI))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+95) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * Math.log1p(Math.expm1((Math.atan((((C - A) - Math.hypot((A - C), B)) / B)) / Math.PI)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.6e+95:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * math.log1p(math.expm1((math.atan((((C - A) - math.hypot((A - C), B)) / B)) / math.pi)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.6e+95)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * log1p(expm1(Float64(atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)) / pi))));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.6e+95], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[Log[1 + N[(Exp[N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.59999999999999994e95

   1. Initial program 13.9%

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

   3. Taylor expanded in A around -inf 76.9%

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

      1. associate-*r/ 76.9%

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

   5. Simplified 76.9%

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

   if -4.59999999999999994e95 < A

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

      2. +-commutative 62.0%

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

      3. unpow2 62.0%

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

      4. unpow2 62.0%

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

      5. hypot-udef 85.4%

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

      6. associate--r+ 84.8%

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

      7. div-inv 84.9%

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

      8. log1p-expm1-u 84.9%

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

   4. Applied egg-rr 85.4%

      \[\leadsto 180 \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.6e+90)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 4.4e-36)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+90) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 4.4e-36) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+90) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 4.4e-36) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.6e+90:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 4.4e-36:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.6e+90)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 4.4e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.6e+90)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 4.4e-36)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.6e+90], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.4e-36], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.5999999999999998e90

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 77.4%

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

      1. associate-*r/ 77.4%

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

   5. Simplified 77.4%

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

   if -2.5999999999999998e90 < A < 4.3999999999999999e-36

   1. Initial program 56.7%

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

   3. Taylor expanded in A around 0 52.5%

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

      1. unpow2 52.5%

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

      2. unpow2 52.5%

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

      3. hypot-def 77.5%

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

   5. Simplified 77.5%

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

   if 4.3999999999999999e-36 < A

   1. Initial program 73.4%

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

   3. Taylor expanded in C around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. +-commutative 72.1%

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

      4. unpow2 72.1%

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

      5. unpow2 72.1%

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

      6. hypot-def 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.6e+90)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (* 180.0 (/ 1.0 (/ PI (atan (/ (- C (+ A (hypot (- A C) B))) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+90) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan(((C - (A + hypot((A - C), B))) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e+90) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan(((C - (A + Math.hypot((A - C), B))) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.6e+90:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (1.0 / (math.pi / math.atan(((C - (A + math.hypot((A - C), B))) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.6e+90)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(Float64(C - Float64(A + hypot(Float64(A - C), B))) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.6e+90)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (1.0 / (pi / atan(((C - (A + hypot((A - C), B))) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.6e+90], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(N[(C - N[(A + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.5999999999999998e90

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 77.4%

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

      1. associate-*r/ 77.4%

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

   5. Simplified 77.4%

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

   if -2.5999999999999998e90 < A

   1. Initial program 61.8%

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

   4. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

      2. associate--l- 85.3%

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

   6. Simplified 85.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+89)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 8.5e-24)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+89) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 8.5e-24) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+89) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 8.5e-24) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5e+89:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 8.5e-24:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 8.5e-24)
		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(B - A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5e+89)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 8.5e-24)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+89], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.5e-24], 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[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.50000000000000006e89

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 77.4%

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

      1. associate-*r/ 77.4%

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

   5. Simplified 77.4%

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

   if -1.50000000000000006e89 < A < 8.5000000000000002e-24

   1. Initial program 57.6%

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

   3. Taylor expanded in A around 0 53.4%

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

      1. unpow2 53.4%

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

      2. unpow2 53.4%

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

      3. hypot-def 78.0%

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

   5. Simplified 78.0%

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

   if 8.5000000000000002e-24 < A

   1. Initial program 72.1%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in B around -inf 79.3%

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

      1. neg-mul-1 79.3%

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

      2. unsub-neg 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.15 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.15e+89)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 5.6e-36)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.15e+89) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 5.6e-36) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.15e+89) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 5.6e-36) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.15e+89:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 5.6e-36:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.15e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 5.6e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.15e+89)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 5.6e-36)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.15e+89], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.6e-36], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.1500000000000001e89

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 77.4%

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

      1. associate-*r/ 77.4%

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

   5. Simplified 77.4%

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

   if -2.1500000000000001e89 < A < 5.6000000000000002e-36

   1. Initial program 56.7%

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

   3. Taylor expanded in A around 0 52.5%

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

      1. unpow2 52.5%

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

      2. unpow2 52.5%

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

      3. hypot-def 77.5%

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

   5. Simplified 77.5%

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

   if 5.6000000000000002e-36 < A

   1. Initial program 73.4%

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

   3. Taylor expanded in C around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. +-commutative 72.1%

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

      4. unpow2 72.1%

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

      5. unpow2 72.1%

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

      6. hypot-def 89.8%

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

   5. Simplified 89.8%

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

      1. expm1-log1p-u 42.4%

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

      2. expm1-udef 42.4%

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

      3. distribute-frac-neg 42.4%

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

      4. atan-neg 42.4%

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

   7. Applied egg-rr 42.4%

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

      1. expm1-def 42.4%

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

      2. expm1-log1p 89.8%

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

      3. associate-*r/ 89.8%

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

      4. distribute-rgt-neg-out 89.8%

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

      5. distribute-lft-neg-in 89.8%

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

      6. metadata-eval 89.8%

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

      7. hypot-def 72.1%

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

      8. unpow2 72.1%

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

      9. unpow2 72.1%

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

      10. +-commutative 72.1%

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

      11. unpow2 72.1%

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

      12. unpow2 72.1%

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

      13. hypot-def 89.8%

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

   9. Simplified 89.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.15 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+89)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+89) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+89) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+89:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+89)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+89], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.8e89

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 77.4%

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

      1. associate-*r/ 77.4%

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

   5. Simplified 77.4%

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

   if -1.8e89 < A

   1. Initial program 61.8%

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

   3. Simplified 85.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 46 \lor \neg \left(A \leq 8 \cdot 10^{+183}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+79)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 1.9e-180)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (if (or (<= A 46.0) (not (<= A 8e+183)))
       (* 180.0 (/ (atan (/ (- (- A) B) B)) PI))
       (* 180.0 (/ (atan (/ (- B A) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+79) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.9e-180) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if ((A <= 46.0) || !(A <= 8e+183)) {
		tmp = 180.0 * (atan(((-A - B) / 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 <= -1.5e+79) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.9e-180) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if ((A <= 46.0) || !(A <= 8e+183)) {
		tmp = 180.0 * (Math.atan(((-A - B) / 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 <= -1.5e+79:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.9e-180:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif (A <= 46.0) or not (A <= 8e+183):
		tmp = 180.0 * (math.atan(((-A - B) / 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 <= -1.5e+79)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.9e-180)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif ((A <= 46.0) || !(A <= 8e+183))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - B) / 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 <= -1.5e+79)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.9e-180)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif ((A <= 46.0) || ~((A <= 8e+183)))
		tmp = 180.0 * (atan(((-A - B) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+79], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e-180], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 46.0], N[Not[LessEqual[A, 8e+183]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - B), $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 4 regimes

2. if A < -1.49999999999999987e79

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 76.2%

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

      1. associate-*r/ 76.2%

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

   5. Simplified 76.2%

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

   if -1.49999999999999987e79 < A < 1.9e-180

   1. Initial program 53.2%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in B around -inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. unsub-neg 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in A around 0 56.0%

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

   if 1.9e-180 < A < 46 or 7.99999999999999957e183 < A

   1. Initial program 73.2%

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

   3. Taylor expanded in C around 0 65.1%

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

      1. associate-*r/ 65.1%

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

      2. mul-1-neg 65.1%

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

      3. +-commutative 65.1%

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

      4. unpow2 65.1%

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

      5. unpow2 65.1%

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

      6. hypot-def 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in A around 0 64.0%

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

   if 46 < A < 7.99999999999999957e183

   1. Initial program 67.8%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in B around -inf 79.9%

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

      1. neg-mul-1 79.9%

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

      2. unsub-neg 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in C around 0 80.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 46 \lor \neg \left(A \leq 8 \cdot 10^{+183}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.9e+31)
   (* 180.0 (/ (atan (/ (+ B C) B)) PI))
   (if (<= B -8.8e-136)
     (* 180.0 (/ (atan (/ (- B A) B)) PI))
     (if (<= B -1.75e-143)
       (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
       (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.9e+31) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (B <= -8.8e-136) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else if (B <= -1.75e-143) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((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 (B <= -3.9e+31) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (B <= -8.8e-136) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else if (B <= -1.75e-143) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / 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 B <= -3.9e+31:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif B <= -8.8e-136:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	elif B <= -1.75e-143:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / 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 (B <= -3.9e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (B <= -8.8e-136)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	elseif (B <= -1.75e-143)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / 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 (B <= -3.9e+31)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (B <= -8.8e-136)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	elseif (B <= -1.75e-143)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.9e+31], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.8e-136], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.75e-143], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $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 4 regimes

2. if B < -3.89999999999999999e31

   1. Initial program 41.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in B around -inf 84.0%

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

      1. neg-mul-1 84.0%

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

      2. unsub-neg 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in A around 0 81.7%

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

   if -3.89999999999999999e31 < B < -8.8000000000000005e-136

   1. Initial program 63.7%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in B around -inf 63.1%

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

      1. neg-mul-1 63.1%

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

      2. unsub-neg 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in C around 0 58.5%

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

   if -8.8000000000000005e-136 < B < -1.75000000000000003e-143

   1. Initial program 28.7%

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

   3. Taylor expanded in A around -inf 100.0%

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

      1. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   if -1.75000000000000003e-143 < B

   1. Initial program 55.8%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in B around inf 65.8%

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

      1. +-commutative 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.05e-95)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.6e+15)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-95) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.6e+15) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-95) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.6e+15) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.05e-95:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.6e+15:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.05e-95)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.6e+15)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.05e-95)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.6e+15)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.05e-95], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e+15], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.05e-95

   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 B around -inf 62.8%

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

   if -1.05e-95 < B < 2.6e15

   1. Initial program 58.7%

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

   3. Taylor expanded in A around inf 39.4%

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

   if 2.6e15 < B

   1. Initial program 50.3%

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

   3. Taylor expanded in B around inf 67.7%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e+79)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 5e+21)
     (* 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 <= -9e+79) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 5e+21) {
		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 <= -9e+79) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 5e+21) {
		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 <= -9e+79:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 5e+21:
		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 <= -9e+79)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 5e+21)
		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 <= -9e+79)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 5e+21)
		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, -9e+79], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e+21], 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 < -8.99999999999999987e79

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 76.2%

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

      1. associate-*r/ 76.2%

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

   5. Simplified 76.2%

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

   if -8.99999999999999987e79 < A < 5e21

   1. Initial program 59.1%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in B around -inf 57.2%

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

      1. neg-mul-1 57.2%

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

      2. unsub-neg 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in A around 0 52.2%

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

   if 5e21 < A

   1. Initial program 70.2%

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

   3. Taylor expanded in A around inf 66.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e+83)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 1.05e-194)
     (* 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 <= -9.5e+83) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.05e-194) {
		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 <= -9.5e+83) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.05e-194) {
		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 <= -9.5e+83:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.05e-194:
		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 <= -9.5e+83)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.05e-194)
		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 <= -9.5e+83)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.05e-194)
		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, -9.5e+83], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e-194], 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 < -9.5000000000000002e83

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 76.2%

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

      1. associate-*r/ 76.2%

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

   5. Simplified 76.2%

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

   if -9.5000000000000002e83 < A < 1.05e-194

   1. Initial program 53.6%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in B around -inf 55.5%

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

      1. neg-mul-1 55.5%

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

      2. unsub-neg 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in A around 0 55.6%

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

   if 1.05e-194 < A

   1. Initial program 70.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in B around -inf 69.9%

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

      1. neg-mul-1 69.9%

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

      2. unsub-neg 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in C around 0 64.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.4 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.4e-96)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.7e+15)
     (* 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 <= -7.4e-96) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.7e+15) {
		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 <= -7.4e-96) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.7e+15) {
		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 <= -7.4e-96:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.7e+15:
		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 <= -7.4e-96)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.7e+15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.4e-96)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.7e+15)
		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, -7.4e-96], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e+15], 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 3 regimes

2. if B < -7.39999999999999972e-96

   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 B around -inf 62.8%

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

   if -7.39999999999999972e-96 < B < 2.7e15

   1. Initial program 58.7%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in B around -inf 54.5%

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

      1. neg-mul-1 54.5%

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

      2. unsub-neg 54.5%

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

   7. Simplified 54.5%

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

   8. Taylor expanded in A around inf 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

   10. Simplified 39.0%

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

   if 2.7e15 < B

   1. Initial program 50.3%

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

   3. Taylor expanded in B around inf 67.7%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.4 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-159)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (* 180.0 (/ 1.0 (/ PI (atan (/ (- C (+ A B)) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-159) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan(((C - (A + B)) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-159) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan(((C - (A + B)) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-159:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (1.0 / (math.pi / math.atan(((C - (A + B)) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(Float64(C - Float64(A + B)) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-159)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	else
		tmp = 180.0 * (1.0 / (pi / atan(((C - (A + B)) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-159], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.00000000000000032e-159

   1. Initial program 49.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 74.0%

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

      1. neg-mul-1 74.0%

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

      2. unsub-neg 74.0%

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

   7. Simplified 74.0%

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

   if -5.00000000000000032e-159 < B

   1. Initial program 55.6%

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

   4. Applied egg-rr 79.1%

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

      1. unpow-1 79.1%

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

      2. associate--l- 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in B around inf 66.0%

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

4. Final simplification 69.3%

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

Alternative 14: 66.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-165)
   (* 180.0 (/ 1.0 (/ PI (atan (/ (+ C (- B A)) B)))))
   (* 180.0 (/ 1.0 (/ PI (atan (/ (- C (+ A B)) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-165) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan(((C + (B - A)) / B))));
	} else {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan(((C - (A + B)) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-165) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan(((C + (B - A)) / B))));
	} else {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan(((C - (A + B)) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-165:
		tmp = 180.0 * (1.0 / (math.pi / math.atan(((C + (B - A)) / B))))
	else:
		tmp = 180.0 * (1.0 / (math.pi / math.atan(((C - (A + B)) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-165)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(Float64(C + Float64(B - A)) / B)))));
	else
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(Float64(C - Float64(A + B)) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-165)
		tmp = 180.0 * (1.0 / (pi / atan(((C + (B - A)) / B))));
	else
		tmp = 180.0 * (1.0 / (pi / atan(((C - (A + B)) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if B < -2e-165

   1. Initial program 49.2%

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

   4. Applied egg-rr 79.4%

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

      1. unpow-1 79.4%

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

      2. associate--l- 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in B around -inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   9. Simplified 74.1%

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

   if -2e-165 < B

   1. Initial program 55.6%

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

   4. Applied egg-rr 79.1%

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

      1. unpow-1 79.1%

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

      2. associate--l- 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in B around inf 66.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-94)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.1e-52)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-94) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.1e-52) {
		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 tmp;
	if (B <= -4e-94) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.1e-52) {
		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):
	tmp = 0
	if B <= -4e-94:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.1e-52:
		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)
	tmp = 0.0
	if (B <= -4e-94)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.1e-52)
		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)
	tmp = 0.0;
	if (B <= -4e-94)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.1e-52)
		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_] := If[LessEqual[B, -4e-94], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.1e-52], 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 3 regimes

2. if B < -3.9999999999999998e-94

   1. Initial program 47.7%

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

   3. Taylor expanded in B around -inf 63.3%

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

   if -3.9999999999999998e-94 < B < 4.09999999999999988e-52

   1. Initial program 61.7%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in B around -inf 58.1%

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

      1. neg-mul-1 58.1%

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

      2. unsub-neg 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in C around inf 37.2%

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

   if 4.09999999999999988e-52 < B

   1. Initial program 48.6%

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

   3. Taylor expanded in B around inf 58.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-159)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-159) {
		tmp = 180.0 * (atan(((C + (B - A)) / 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 (B <= -5e-159) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / 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 B <= -5e-159:
		tmp = 180.0 * (math.atan(((C + (B - A)) / 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 (B <= -5e-159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / 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 (B <= -5e-159)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-159], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.00000000000000032e-159

   1. Initial program 49.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 74.0%

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

      1. neg-mul-1 74.0%

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

      2. unsub-neg 74.0%

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

   7. Simplified 74.0%

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

   if -5.00000000000000032e-159 < B

   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. Step-by-step derivation

   3. Simplified 72.5%

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

   5. Taylor expanded in B around inf 66.0%

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

      1. +-commutative 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 69.3%

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

Alternative 17: 45.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.22 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.22e-135)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.2e-91)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.22e-135) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.2e-91) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.22e-135) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.2e-91) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.22e-135:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.2e-91:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.22e-135)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.2e-91)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.22e-135)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.2e-91)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.22e-135], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.2e-91], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.22e-135

   1. Initial program 49.5%

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

   3. Taylor expanded in B around -inf 59.7%

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

   if -1.22e-135 < B < 9.19999999999999982e-91

   1. Initial program 62.4%

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

      1. add-log-exp 61.6%

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

      2. associate-*l/ 61.6%

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

      3. *-un-lft-identity 61.6%

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

      4. unpow2 61.6%

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

      5. unpow2 61.6%

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

      6. hypot-def 85.4%

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

   4. Applied egg-rr 85.4%

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

   5. Taylor expanded in C around inf 28.8%

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

      1. associate-*r/ 28.8%

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

      2. distribute-rgt1-in 28.8%

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

      3. metadata-eval 28.8%

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

      4. mul0-lft 28.8%

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

      5. metadata-eval 28.8%

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

      6. div0 28.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   7. Simplified 28.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 9.19999999999999982e-91 < 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 55.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.22 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.2 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.2e-89) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.2e-89) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.2e-89) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.2e-89:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4.2e-89)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 4.2e-89)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.2e-89], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 4.2000000000000002e-89

   1. Initial program 55.1%

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

      1. add-log-exp 54.7%

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

      2. associate-*l/ 54.7%

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

      3. *-un-lft-identity 54.7%

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

      4. unpow2 54.7%

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

      5. unpow2 54.7%

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

      6. hypot-def 81.9%

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in C around inf 15.5%

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

      1. associate-*r/ 15.5%

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

      2. distribute-rgt1-in 15.5%

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

      3. metadata-eval 15.5%

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

      4. mul0-lft 15.5%

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

      5. metadata-eval 15.5%

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

      6. div0 15.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   7. Simplified 15.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 4.2000000000000002e-89 < 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 55.4%

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

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.2 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 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 53.0%

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

3. Taylor expanded in B around inf 20.7%

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

4. Final simplification 20.7%

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

Reproduce

herbie shell --seed 2024024 
(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)))